THERMODYNAMICS 



OF THE 



STEAM-ENGINE 



AND 



OTHER HEAT-ENGINES 



BY 

CECIL H. PEABODY 

PROFESSOR OF NAVAL ARCHITECTURE AND MARINE ENGINEERING, 
MASSACHUSETTS INSTITUTE OF TECHNOLOGY 



FIFTH EDITION, REWRITTEN 

FIRST THOUSAND 



NEW YORK 

JOHN WILEY & SONS 

London : CHAPMAN & HALL, Limited 
1907 



< 



< 



-S"' 



I UiSHhHY of CONGRESS 
Two Cooles Received 

OCT 18 »9or 

Copyngh! Entry 

CUsIa XXc.,N6. 

COPY B 



Copyright 1889, 1898, 1907 

BY 

CECIL H. PEABODY 



y^^Jf// 



PREFACE TO FIFTH EDITION. 



When this work was first in preparation the author had before 
liim the problem of teaching thermodynamics so that students in 
engineering could use the results immediately in connection with 
experiments in the Engineering Laboratories of the Massachu- 
setts Institute of Technology. The acceptance of the book by 
teachers of engineering appears to justify its general plan, which 
will be adhered to now that the development of engineering calls 
for a complete revision. 

The author is still of the opinion that the general mathematical 
presentation due to Clausius and Kelvin is most satisfactory and 
carries with it the ability to read current thermodynamic inves- 
tigations by engineers and physicists. At the same time it is 
recognized that recent investigations of superheated steam are 
presented in such a way as to narrow the applications of the 
general method so that there is justification for those who prefer 
special methods for those appHcations. To provide for both 
views of this subject, the general mathematical discussion is 
presented in a separate chapter, which may be omitted at the 
first reading (or altogether), provided that the special methods, 
which also are given in the proper places, are taken to be sufficient. 

The first edition presented fundamental data not generally 
accepted at that time, so that it was considered necessary to 
justify the data by giving the derivation at length; much of this 
matter, which is no longer new, is removed to an appendix, to 
relieve the student of discussions that must appear unnecessary 
and tedious. 

The introduction of the steam-turbine has changed adiabatic 
calculations for steam, from an apparent academic abstraction, to 
a common necessity. To meet this changed condition, the Tables of 

iii 



IV PREFACE 

Properties of Saturated Steam have had added to them columns 
of entropies of vaporization; and further there has been 
computed a table of the quahty (or dryness factor) the heat 
contents and volume at constant entropy, for each degree 
Fahrenheit. This table will enable the computer to deter- 
mine directly the efifect of adiabatic expansion to any pres- 
sure or volume, and to calculate with ease the external work 
in a cylinder or the velocity of flow through an orifice or nozzle 
including the effect of friction; and also to tietermine the distri- 
bution of work and pressure for a steam-turbine. For the 
greater part of practical work this table may be used without 
interpolation, or by interpolation greater refinement may be had. 

Advantage is taken of recent experiments on the properties of 
superheated steam and of the application to tests on engines to 
place that subject in a more satisfactory condition. Attention 
is also given to the development of internal combustion engines 
and to the use of fuel and blast-furnace gas. A chapter is given 
on the thermodynamics of the steam-turbine with current method 
of computation, and results of tests. 

So far as possible the various chapters are made independent, 
so that individual subjects, such as the steam-engine, steam-tur- 
bine, compressed-air and refrigerating machines, may be read 
separately in the order that may commend itself. 



PREFACE TO FIRST EDITION. 



This work is designed to give instruction to students in 
technical schools in the methods and results of the application 
of thermodynamics to engineering. While it has been considered 
desirable to follow commonly accepted methods, some parts 
differ from other text-books, either in substance or in manner of 
presentation, and may require a few words of explanation. 

The general theory or formal presentation of thermodynamics 



PREFACE V 

is that employed by the majority of writers, and was prepared 
with the view of presenting clearly the difficulties inherent in the 
subject, and of giving famiHarity with the processes employed. 

In the discussion of the properties of gases and vapors the 
original experimental data on which the working equations, 
whether logical or empirical, must be based are given quite 
fully, to afford an idea of the degree of accuracy attainable in 
calculations made with their aid. Rowland's determination of 
the mechanical equivalent of heat has been adopted, and with it 
his determination of the specific heat of water at low tempera- 
tures. The author's "Tables of the Properties of Saturated 
Steam and Other Vapors" were ^calculated to accompany this 
work, and may be considered to be an integral part of it. 

The chapters on the flow of gases and vapors and on the 
injector are beheved to present some novel features, especially 
in the comparisons with experiments. 

The feature in which this book differs most from similar 
works is in the treatment of the steam-engine. It has been 
deemed advisable to avoid all approximate theories based on 
the assumption of adiabatic changes of steam in an engine 
cyUnder, and instead to make a systematic study of steam- 
engine tests, with the view of finding what is actually known on 
the subject, and how future investigations and improvements 
may be made. For this purpose a large number of tests have 
been collected, arranged, and compared. Special attention is 
given to the investigations of the action of steam in the cylinder 
of an engine, considerable space being given to Hirn's researches 
and to experiments that provide the basis for them. Directions 
are given for testing engines, and for designing simple and com- 
pound engines. 

Chapters have been added on compressed-air and refrigerating 
machines, to provide for the study of these important subjects 
in connection with the theory of thermodynamics. 

Wherever direct quotations have been made, references have 
been given in foot-notes, to aid in more extended investigations. 
It does not appear necessary to add other acknowledgment of 



VI PREFACE 



assistance from well-known authors, further than to say that 
their writings have been diUgently searched in the preparation 
of this book, since any text-book must be largely an adaptation of 
their work to the needs of instruction. 



C. H. P. 



Massachusetts Institute of Technology, 
May, 1889. 



PREFACE TO FOURTH EDITION. 



A THOROUGH revision of this work has been made to bring 
it into accord with more recent practice and to include later 
experimental work. Advantage is taken of this opportunity to 
make changes in matter or in arrangement which it is beHeved 
will make it more useful as a text- book. 

C. H. P. 
Massachusetts Institute of Technology 
July, 1898. 



TABLE OF CONTENTS. 



CHAPTER PAGK 

I. Thermal Capacities ...,.- i 

II. First Law of Thermodynamics ............. 13 

III. Second Law of ThermTodynamics 22 

IV. General Thermodynamic Method 43 

V. Perfect Gases . . . 54 

VI. Saturated Vapor ' „ 76 

VII. Superheated Vapors , 100 

VIII. The Steam-engine 128 

IX. Compound Engines , . . . . 156 

X. Testing Steam-engines 183 

XI. Influence of the Cylinder Walls jgg 

XII. Economy of Steam-engines 237 

XIII. Friction of Engines 285 

XIV. Internal-Combustion Engines ............... 298 

XV. Compressed Air 3^8 

XVI. Refrigerating Machines , » . . . . 396 

XVII. Flow of Fluids .. ..... , 423 

XVIII. Injectors .... , . » 447 

XIX. Steam-turbines •.,...,.,..,... 472 



THERMODYNAMICS OF THE STEAM-ENGINE, 



CHAPTER I. 

THERMAL CAPACITIES. 

The object of thermodynamics, or the mechanical theory of 
heat, is the solution of problems involving the action of heat, 
and, for the engineer, more especially those problems presented 
by the steam-engine and other thermal motors. The substances 
in which the engineer has the most interest are gases and vapors, 
more especially air and steam. Fortunately an adequate treat- 
ment can be given of these substances for engineering purposes. 

First General Principle. — In the development of the theor)^ 
of thermodynamics it is assumed that if any two characteristics 
or properties of a substance are known these two, treated as 
independent variables, will enable us to calculate any third 
property. 

As an example, we have from the combination of the laws of 
Boyle and Gay-Lussac the general equation for gases, 

pv = RT, 

in which p is the pressure, v is the volume, T is the absolute 
temperature by the air-thermometer, and i? is a constant which 
for air has the value 53.22 when English units are used. It is 
probable that this equation led to the general assumption just 
quoted. That assumption is purely arbitrary, and is to be justi- 
fied by its results. It may properly be considered to be the first 
general principle of the theory of thermodynamics; the other 
two general principles are the so-called first and second laws of 
thermodynamics, which will be stated and discussed later. 



2 THERMAL CAPACITIES 

Characteristic Equation. — An equation which gives the 
relations of the properties of any substance is called the charac- 
teristic equation for that substance. The properties appearing 
in a characteristic equation are commonly pressure, volume, 
and temperature, but other properties may be used if convenient. 
The form of the equation must be determined from experiments, 
either directly or indirectly. 

The characteristic equation for a gas is, as already quoted, 

pv = RT. 

The characteristic equation for an imperfect gas, like super- 
heated steam, is likely to be more complex; for example, the 
equation given by Knoblauch, Linde, and Klebe is 

pv=BT-p{i+ ap) [c {^-d\- 

On the other hand, the properties of saturated steam, especially 
if mixed with water, cannot be represented by a single equation. 

Specific Pressure. — The pressure is assumed to be a hydro- 
static pressure, such as a fluid exerts on the sides of the con- 
taining vessel or on an immersed body. The pressure is 
consequently the pressure exerted hy the substance under con- 
sideration rather than the pressure on that substance. For 
example, in the cylinder of a steam-engine the pressure of the 
steam is exerted on the piston during the forward stroke and 
does work on the piston; during the return stroke, when the 
steam is expelled from the cylinder, it still exerts pressure on 
the piston and abstracts work from it. 

For the purposes of the general theory pressures are 
expressed in terms of pounds on the square foot for the English 
system of units. In the metric system the pressure is expressed 
in terms of kilograms on the square metre. A pressure thus 
expressed is called the specific pressure. In engineering practice 
other terms are used, such as pounds on the square inch, inches 
of mercury, millimetres of mercury, atmospheres, or kilograms 
on the square centimetre. 



TEMPERATURE 3 

Specific Volume. — It is convenient to deal with one unit of 
weight of the substance under discussion, and to coAsider the 
volume occupied by one pound or one kilogram of the substance; 
this is called the specific volume, and is expressed in cubic feet or 
in cubic metres. The specific volume of air at freezing-point 
and imder the normal atmospheric pressure is 12.39 cubic feet; 
the specific volume of saturated steam at 2i2°F. is 26.6 cubic 

feet ; and the specific volume of water is about - — ■ , or nearly 

62.4 

0.016 of a cubic foot. 

Temperature is commonly measured by aid of a mercurial 
thermometer which has for its reference-points the freezing- 
point and boiling-point of water. A centigrade thermometer 
has the volume of the stem between the reference- points divided 
into one hundred equal parts called degrees. The Fahrenheit 
thermometer differs from the centigrade in having one hundred 
and eighty degrees between the freezing-point and the boiling- 
point, and in having its zero thirty-two degrees below freezing. 

The scale of a mercurial thermometer is entirely arbitrary, 
and its indications depend on the relative expansion of glass and 
mercury. Indications of such thermometers, however carefully 
made, differ appreciably, mainly on account of the varying 
nature of the glass. For refined investigations thermometric 
readings are reduced to the air- thermometer, which has the 
advantage that the expansion of air is so large compared with 
the expansion of glass that the latter has little or no effect. 

It is convenient in making calculations of the properties of 
air to refer temperatures to the absolute zero of the scale of the 
air-thermometer. To get a conception of what is meant by this 
expression we may imagine the air-thermometer to be made of 
a uniform glass tube with a proper index to show the volume 
of the air. The position of the index may be marked at boiling- 
point and at freezing-point as on the mercurial thermometer, 
and the space between may be divided into one hundred parts 
or degrees. If the graduations are continued to the closed end 
of the tube there will be found to be 273 of them. It will be 



4 THERMAL CAPACITIES 

shown later that there is reason to suppose that the absolute 
zero of temperature is 273° centigrade below the freezing-point 
of water. Speculations as to the meaning of absolute zero and 
discussions concerning the nature of substances at that temper- 
ature are not now profitable. It is sufficient to know that 
equations are simplified and calculations are facilitated by this 
device.. For example, if temperature is reckoned from the 
arbitrary zero of the centigrade thermometer, then the charac- 
teristic equation for a perfect gas becomes 



-£+') 



R, 



in which a is the coefficient of dilatation and — = 273 nearly. 

a 

In order to distinguish the absolute temperature from the 
temperature by the thermometer we shall designate the former 
by T and the latter by t, bearing in mind that 

T = t -\- 273° centigrade, 
T = t + 459.5 Fahrenheit. 

Physicists give great weight to the discussion of a scale of 
temperature that can be connected with the fundamental units 
of length and weight like the foot and the pound. Such a scale, 
since it does not depend on the properties of any substance 
(glass, mercury, or air), is considered to be the absolute scale of 
temperature. The differences between such a scale and the 
scale of the air-thermometer are very small, and are difficult to 
determine, and for the engineer are of little moment. At the 
proper place the conception of the absolute scale can be easily 
stated. 

Graphical Representation of the Characteristic Equation. — 
Any equation with three variables may be represented by a 
geometrical surface referred to co-ordinate axes, of which surface 
the variables are the co-ordinates. In the case of a perfect gas 
which conforms to the equation 

pv = RT, 



STANDARD TEMPERATURE 5 

the surface is such that each section perpendicular to the axis 
of r is a rectangular hyperbola (Fig. i). 

Returning now to the general case, 
it is apparent that the characteristic /, 

equation of any substance may be repre- /'Tw 
sented by a geometrical surface referred \ oA \ 
to co-ordinate axes, since the equation is j \ 
assumed to contain only three variables; j /V/""^"'^'^'^ 
but the surface will in general be less ij/^ ! /- 

simple in form than that representing the ' ^~~ 

combined laws of Boyle and Gay-Lussac. 

If one of the variables, as T, is given a special constant value, 
it is equivalent to taking a section perpendicular to the axis of 
T\ and a plane curve will be cut from the surface, which may 
be conveniently projected on the (^, v) plane. The reason for 
choosing the (^, v) plane is that the curves correspond with 
those drawn by the steam-engine indicator. 

Considerable use is made of such thermal curves in explaining 
thermodynamic conceptions. As a rule, a graphical process 
or representation is merely another way of presenting an idea 
that has been, or may be, presented analytically; there is, how- 
ever, an advantage in representing a condition or a change to 
the eye by a diagram, especially in a discussion which appears 
to be abstract. A number of thermal curves are explained on 
page 16. 

Standard Temperature. — For many purposes it is convenient 
to take the freezing-point of water for the standard temperature, 
since it is one of the reference-points on the thermometric scale; 
this is especially true for air. But the properties of water change 
rapidly at and near freezing-point and are very imperfectly 
known. It has consequently become customary to take 62° F. 
for the staildard temperature for the English system of units; 
there is a convenience in this, inasmuch as the pound and yard 
are standards at that temperature. For the metric system 15° C. 
is used, though the kilogram and metre are standards at freezing- 
point. 



O THERMAL CAPACITIES 

Thermal Unit. — Heat is measured in calories or in British 
thermal units (b. t. u.). A British thermal unit is the heat 
required to raise one pound of water from 62° F. to 63° F.; in 
like manner a calorie is the heat required to raise one kilogram 
of water from 15° C. to 16° C. 

Specific Heat is the number of thermal units required to raise 
a unit of weight of a given substance one degree of temperature. 
The specific heat of water at the standard temperature is, of 
course, unity. 

If the specific heat of a given substance is constant, then the 
heat required to raise one pound through a given range of tem- 
perature is the product of the specific heat by the increase of 
temperature. Thus if c is the specific heat and ^ — /j is the range 
of temperature the heat required is 

Q = c (t — /i), and c = — ^— • 



If the specific heat varies the amount of heat must be obtained 
by integration — that is," 



Q = J cdt, 



and conversely 

dQ 



dt 



It is customary to distinguish two specific heats for perfect 
gases; specific heat at constant pressure and specific heat at 
constant volume, which may be represented by 



= ©/"'^^" = (?)/ 



the subscript attached to the parenthesis indicates the property 
which is constant during the change. It is evident that the 
specific heats just expressed are partial differential coefficients. 

Latent Heat of Expansion is the amount of heat required to 
increase the volume of a unit of weight of the substance by one 



EFFECTS PRODUCED BY HEAT 7 

cubic foot, or one cubic metre, at constant temperature. It 
may be represented by 

\Bv/t 



I 



Thermal Capacities. — The two specific heats and the latent 
heat of expansion are known as thermal capacities. It is cus- 
tomary to use three other properties suggested by those just 
named which are represented as follows: 

The first represents the amount of heat that must be applied 
to one pound of a substance (such as air) to increase the pressure 
by the amount of one pound per square foot at constant tem- 
perature; this property is usually negative and represents the 
heat that must be abstracted to prevent the temperature from 
rising. The other two can be defined in like manner if desired, 
but it is not very important to state the definitions nor to try to 
gain a conception as to what they mean, as it is easy to express 
them in terms of the first three, for which the conceptions are 
not difficult. They have no names assigned to them, which is, 
on the whole, fortunate, as, of the first three, two have names that 
have no real significance, and the third is a misnomer. 

General Equations of the Effects Produced by Heat. — In 
order to be able to compute the amount of heat required to 
produce a change in a substance by aid of the characteristic 
equation, it is necessary to admit that there is a functional rela- 
tion between the heat applied and some two of the properties 
that enter into the characteristic equation. It will appear later 
in connection with the discussion of the first law of thermody- 
namics that an integral equation cannot in general be written 
directly, but we may write a differential equation in one of the 
three following forms: 



«-(l)/-(i),*. 



THERMAL CAPACITIES 






or substituting for the partial differential coefficients the letters 
which have been selected to represent them, 

dQ = c^dt + Idv (i) 

dQ = Cpdt + mdp (2) 

dQ = ndp + odv (3) 

This matter may perhaps be 
clearer if it is presented graph- 
ically as in Fig. 2, where ah is 
intended to represent the path 
of a point on the characteristic 
surface in consequence of the 
addition of the heat dQ. There 
will in general be a change of 
temperature volume and pres- 
sure as indicated on the figure. 
Now the path ah, which 
for a small change may 
be considered to be a straight 
line, will be projected on 
the three planes at a'V , a"h" and a'^'h'" . The projection on the 
iy^T) plane may be resolved into the components ^v and ^T\ 
the first represents a change of volume at constant temperature 
requiring the heat Idv, and the second represents a change of tem- 
perature at constant volume requiring the heat c^dt. Conse- 
quently the heat required for the change in terms of the volume 
and temperature is 




dQ = c^dt + Idv. 



RELATIONS OF THE THERMAL CAPACITIES 9 

Relations of the Thermal Capacities. — The three equations 
(5), (6), and (7), show the changes produced by the addition of 
an amount of heat dQ to a unit of weight of a substance, the 
difference coming from the methods of analyzing the changes. 
We may conveniently find the relations of the several thermal 
capacities by the method of undetermined coefficients. Thus 
equating the right-hand members of equations (5) and (6), 

c^dt + Idv = Cpdt + mdp (4) 

From the characteristic equation we shall have in general 

v = F(p, T), 

as, for example, for air we have 

RT 

p 

and consequently we may write 

which substituted in equation (4) gives, 

-j-dt + -^dp\' 
c, + Ij-) di + I ^dp . . (5) 

It will be noted that, as T differs from t only by the addition 
of a constant, the differential dt may be used in all cases, whether 
we are dealing with absolute temperatures, or temperatures on 
the ordinary thermometer. 

In equation (5) p and T are independent variables, and each 
may have all possible values; consequently we may equate Hke 
coefficients. 



lO THERMAL CAPACITIES 

Also, equating the remaining coefficients, 

^8^ = ^" (7) 

If the characteristic equation is solved for the pressure we 
shall have 

p = F, (T, v\ 

so that 

'^^=&-* + &'^^ w 

which substituted in equation (4) gives 

Cpdt + m l-~ dt + ~-dv] = c^dt + Idv, 

/. icp + m -~] dt -\- m~dv = c^dt + Idv, 

Equating like coefficients, 

Cp + m-^^ == c, (9) 

- ^~§^= Cp — c„ . . . . (10) 

From equations (2) and (3) 

Cpdt + mdp = ndp + odv , . . . (11) 

and from an equation 

T = F, (V, p) 

ht , 3/ , 

which latter substituted in equation (11) gives 

^t , U ^ . . n 

Cp~ dv + Cp ^- dp + mdp = ndp + odv. 

Equating coefficients of dv, 

= Cp-^ . , , . . . (12) 



RELATIONS OF THE THERMAL CAPACITIES ii 

Finally, from equations (i) and (3), 

c^dt + Idv = ndp -{- odv (13) 

Substituting for dt as above, 

CvT~~ dv + c„-r— dp -{- Idv = ndp + odv, 
ov op 

Equating coefficients of dp, 

^ = ^«S^ • • (14) 

For convenience the several relations of the thermal capacities 
may be assembled as follows : 

Zv Sp 

"*" '"Sp' " ' '" s, 

"^^^^ 

They are the necessary algebraic relations of the literal func- 
tions growing out of the first general principle, and are inde- 
pendent of the scale of temperature, or of any other theoretical 
or experimental principle of thermodynamics other than the one 
already stated — namely, that any two properties of a given 
substance, treated as independent variables, are sufficient to 
allow us to calculate any third property. 

Of the six thermal capacities the specific heat at constant 
pressure is the only one that is commonly known by direct 
experiment. For perfect gases this thermal capacity is a con- 
stant, and, further, the ratio of the specific heats 



is a constant, so that c^ is readily calculated. The relations of 
the thermal capacities allow us to calculate values for the. 



12 THERMAL CAPACITIES 

Other thermal capacities, /, m, n, and o, provided that we can 
first determine the several partial differential coefficients which 
appear in the proper equations. But for a perfect gas the 
characteristic equation is 

pv = RT, 
from which we have 

^_ R, ^ __ R. 

Si " p' St " V ' 

Bp ~ R' 8v " r' 

Substituting these values in the equations for the thermal 
capacities, we have 

^ = I fe — ^r) ; — w = ^ (^p- Cv) ; 
V p 

by aid of which the several thermal capacities may be calculated 
numerically, or, what is the usual procedure, may be represented 
in terms of the specific heats. 



CHAPTER II. 

FIRST LAW OF THERMODYNAMICS. 

The formal statement of the first law of thermodynamics is: 

Heat and mechanical energy are mutually convertible^ and 
heat requires for its production and produces by its disappearance 
a definite number of units of work for each thermal unit. 

This law, which may be considered to be the second general 
principle of thermodynamics, is the statement of a well-deter- 
mined physical fact. It is a special statement of the general 
law of the conservation of energy, i.e., that energy may be trans- 
formed from one form to another, but can neither be created 
nor destroyed. It should be stated, however, that the general 
law of conservation of energy, though universally accepted, has 
not been proved by direct experiment in all cases; there may be 
cases that are not susceptible of so direct a proof as we have for 
the transformation of heat into work. 

The best determinations of the mechanical equivalent of heat 
were made by Rowland, whose work will be considered in detail 
in connection with the properties of steam and water. From 
his work it appears that 778 foot-pounds of work are required to 
raise one pound of water from 62° to 63° Fahrenheit; this value 
of the mechanical equivalent of heat is now commonly accepted 
by engineers, and is verified by the latest determinations by 
Joule and other experimenters. 

The values of the mechanical equivalent of heat for the Eng- 
lish system and for the metric system are: 

I B. T. u. = 778 foot-pounds. 

I calorie = 426.9 metre-kilograms. 

This physical constant is commonly represented by the letter 
J] the reciprocal is represented by A, 

13 



14 FIRST LAW OF THERMODYNAMICS 

In older works on thermodynamics the values of J are com- 
monly quoted as 772 for the English system and 424 for the 
metric system. The error of these values is about one per cent. 

Effects of the Transfer of Heat. — Let a quantity of any sub- 
stance of which the weight is one unit — i.e., one pound or one 
kilogram — receive a quantity of heat dQ. It will, in general, 
experience three changes, each requiring an expenditure of 
energy. They are: (i) The temperature will be raised, and, 
according to the theory that sensible heat is due to the vibra- 
tions of the particles of the body, the kinetic energy will be 
increased. Let dS represent this change of sensible heat or 
vibration work expressed in units of work. (2) The mean 
positions of the particles will be changed; in general the body 
will expand. Let dl represent the units of work required for 
this change of internal potential energy, or work of disgregation. 
(3) The expansion indicated in (2) is generally against an exter- 
nal pressure, and to overcome the same — that is, for the change 
in external potential energy — there will be required the work 

If during the transmission no heat is lost, and if no heat is 
transformed into other forms of energy, such as sound, electricity, 
etc., then the first law of thermodynamics gives 

dQ = A{dS ^- dl -^ dW) (15) 

It is to be understood that any or all of the terms of the equa- 
tion may become zero or may be negative. If all the terms 
become negative heat is withdrawn instead of added, and dQ is 
negative. It is not easy to distinguish between the vibration 
work and the disgregation work, and for many purposes it is 
unnecessary; consequently they are treated together under the 
name of intrinsic energy, and we have 

dQ = A (dS + dl + dW) = A(dE + dW) . . (16) 

The inner work, or intrinsic energy, depends on the state of 
the body, and not at all on the manner by which it arrived at 



EFFECTS OF THE TRANSFER OF HEAT 15 

that state; just as the total energy of a falhng body, with refer- 
ence to a given plane consisting of kinetic energy and potential 
energy, depends on the velocity of the body and the height 
above the plane, and not on the previous history of the body. 

The external work is assumed to be done by a fluid-pres- 
sure; consequently 

dW = pdv (17) 



W 



, pdv (18) 



where v^ and v^ are the final and initial volumes. 

In order to find the value of the integral v in equation (18) it 
is necessary to know the manner in which the pressure varies 
with the volume. Since the pressure may vary in different ways, 
the external work cannot be determined from the initial and 
final states of the body; consequently the heat required to effect 
a change from one state to another depends on the manner in 
which the change is effected. 

Assuming the law of the variation of the pressure and volume 
to be known, we may integrate thus: 

Q = A (e, -E,+ £' pdv) .... (19) 

In order to determine E for any state of a body it would be 
necessary to deprive it entirely of vibration and disgregation 
energy, which would of course involve reducing it to a state of 
absolute cold; consequently the direct determination is impossi- 
ble. However, in all our work the substances operated on are 
changed from one state to another, and in each state the intrinsic 
energy depends on the state only; consequently the change of 
intrinsic energy may be determined from the initial and final 
states only, without knowing the manner of change from one to 
the other. 

In general, equations will be arranged to involve differences 



i6 



FIRST LAW OF THERMODYNAMICS 



of energy only, and the hypothesis involved in a separation into 
vibration and disgregation v^^ork avoided. 

Thermal Lines. — The external work can be determined only 
when the relations of p and v are known, or, in general, when 
the characteristic equation is known. It has already been 
shown that in such case the equation may be represented by a 
geometrical surface, on which so-called thermal lines can be 
drawn representing the properties of the substance under con- 
sideration. These lines are commonly projected on the (/>, v) 
plane. It is convenient in many cases to find the relation of p 
and V under a given condition and represent it by a curve drawn 
directly on the (^, v) plane. 

Lines of Equal Pressure. — The change of 
condition takes place at constant pressure, and 
consists of a change of volume, as represented in 
Fig, 3. The tracing- point moves from a^ to a^, 
and the volume changes from v^ to v^. The 
work done is represented by the rectangular area 
under a^a^, or by 



Fig. 3. 



w 



r 



dv = p(v^ — v^) 



(20) 



During the change the temperature may or may not change; 
the diagram shoWs nothing concerning it. 

Lines of Equal Volume. — The pressure in- 
creases at constant volume, and the tracing-point 
moves from a^ to a^. The temperature usually 
increases meanwhile. Since dv is zero. 



W 



,^ Pdv = o 



(21) 



Fig. 4. 



Isothermal Lines, or Lines of Equal Temperature. — The 

temperature remains constant, and a line is drawn, usually 
convex, toward the axis OV. The pressure of a mixture of a 



ADIABATIC LINES 



17 



p 


ttl 






\<a2 







V' 



liquid and its vapor is constant for a given temperature; con- 
sequently the isothermal for such a mixture is a line of equal 
pressure, represented by Fig. 3. The iso- 
thermal of a perfect gas, on the other hand, is 
an equilateral hyperbola, as appears from the 
law of Boyle, which may be written 

pV = C. Fig. 5. 

Isodynamic or Isoenergic Lines are lines representing changes 
during which the intrinsic energy remains constant. Conse- 
quently all the heat received is transformed into external work. 
It will be seen later that the isodynamic and isothermal lines 
for a gas are the same. 

Adiabatic Lines. — A very important problem in thermo- 
dynamics is to determine the behavior of a substance when a 
change of condition takes place in a non-conducting vessel. 
During the change — for example, an increase of volume or 
expansion — some of the heat in the substance may be changed 
into work; but no heat is transferred to or from the substance 
through the walls of the containing vessel. Such changes are 
called adiabatic changes. 

Very rapid changes of dry air in the cylinder of an air-com- 
pressor or a compressed-air engine are very nearly adiabatic. 
Adiabatic changes never occur in the cylinder of a steam-engine 
on account of the rapidity with which steam is condensed on or 
vaporized from the cast-iron walls of the cylinder. 

Since there is no transmission of heat to (or from) the working 
substance, equation (19) becomes 

pdv) .... (22) 

E,-E,=£jpdv (23) 

that is, the external work is done wholly at the expense of the 
intrinsic energy of the working substance, as must be the case 
in conformity with the assumption of an adiabatic change. 



i8 



FIRST LAW OF THERMODYNAMICS 




Fig. 6. 



Relation of Adiabatic and Isothermal Lines. ^- An important 

property of adiabatic lines can be shown to advantage at this 

place, namely, that such a line 
is steeper than an isothermal 
line on the {p, v) plane where 
they cross, as represented in 
Fig. 6. The essential feature of 
adiabatic expansion is that no 
heat is supplied and that conse- 
quently the external work of 
expansion is done at the expense 
of the intrinsic energy which 
consequently decreases. The 
intrinsic energy is the sum of 
the vibration energy and the 
disgregation energy, both of 
which in general decrease during an adiabatic expansion; in partic- 
ular the decrease of vibration energy means a loss of temperature. 
Conversely an adiabatic compression is accompanied by an in- 
crease of temperature. If an isothermal compression is repre- 
sented by ch, then an adiabatic compression will be represented 
by a steeper hne like ca, crossing the constant pressure line ha to 
the right of h, and thus indicating that at that pressure there is 
a greater volume, as must be the case for a body which expands 
during a rise of temperature at constant pressure. 

It is very instructive to note the relation of these lines on the 
surface which represents the characteristic equation for a perfect 
gas. In Fig. 6, which is an isometric projection, the general 
form of the surface can be recognized from the following condi- 
tions : — a horizontal section representing constant pressure 
cuts the surface in a straight line which indicates that the volume 
increases proportionally to the absolute temperature, and this 
line is projected as a horizontal line on the {p, v) plane; a vertical 
section parallel to the {p, t) plane shows that the pressure in 
this case increases as the absolute temperature, and the line of 
intersection with the surface is projected as a vertical line on the 



THERMAL LINES AND THEIR PROJECTIONS 



19 



{pi '^) plane; finally vertical sections parallel to the {p, v) plane 
are rectangular hyperbolae which are projected in their true 
form on the {p, v) plane. If AC is an adiabatic curve on the 
characteristic surface, its loss of temperature is properly repre- 
sented by the fact that it crosses a series of isothermals in passing 
from A to C; ^^ is a line of constant pressure showing a decrease 
of temperature between the isothermals through A and through 
C; finally the projection of ABC on to the {p, v) plane shows that 
the adiabatic line ac is steeper than the isothermal line he. 
Attention should be called to the fact that the first statement 
of this relation is the more general as it holds for all substances 
that expand with rise of temperature at constant pressure what- 
ever may be the form of the characteristic equation. 

Thermal Lines and their Projections. — The treatment given 
of thermal lines is believed to be the simplest and to present 
the features that are most useful in practice. There is, how- 
ever, both interest and instruction in Considering their relation 
in space and their projections on the three thermal planes. It 
is well to look attentively at Fig. 6, which is a correct isometric 
projection of the characteristic surface of a gas following the 
law of Boyle and Gay-Lussac, noting that every section by a 
plane parallel to the {p, v) plane is 
a rectangular hyperbola which has 
the same form in space and when 
projected on the {p, v) plane. The 
sections by a plane parallel to the 
{p, t) plane are straight fines and are 
of course projected as straight lines 
on that plane and on the (_/>, v) plane; 
in like manner the sections by planes 
parallel to the (/, v) plane are straight 
lines. The adiabatic fine in space 
and as projected on the {p, v) plane is probably drawn a little 
too steep, but the divergence from truth is not evident to the eye. 

In Fig. 7 the same method of projection is used, but other 
fines are added together with their projections on the several 




20 



FIRST LAW OF THERMODYNAMICS 



planes. Beginning at the point a in space the line ah is an 
isothermal which is projected as a rectangular hyperbola a'h^ 
on the (p, v) plane, and as straight lines a^'b^^ and a'"h"' on 
the (/>, /) and (/, v) plane. The adiabatic hne ac is steeper 
than the isothermal, both in space and on the (^, v) plane, as 
already explained; it is projected as a curve {a"c" or a"'c'") on 
the other planes. The section showing constant pressure is 
represented in space by the straight line ae which projected on 
the (^, t) plane is parallel to the axis <?/, and on the (^, v) 
plane is parallel to the line itself in space; on the (^, v) plane it is 
horizontal, as shown in Fig. 3. In much the same way ad is the 
section by a plane parallel to the (/, v) plane, and a'd\ a"d'' 
and a"'d'" are its projections. 

Graphical Representations of Change of Intrinsic Energy. — 
Professor Rankine first used a graphical method of representing 
a change of intrinsic energy, employing adiabatic lines only, as 
follows: 

Suppose that a substance is originally in the state A (Fig. 8), 
and that it expands adiabatically; then the external work is done 
at the expense of the intrinsic energy; hence if the expansion 
has proceeded to A^ the area AA^a^a, which represents the 
external work, also represents the change of intrinsic energy. 
Suppose that the expansion were to continue indefinitely; then 
the adiabatic will approach the axis OV 
indefinitely, and the area representing the 
work will be included between the curve Aa 
3 produced indefinitely, the ordinate Aa, and 
^ the axis OV; this area will represent all the 
work that can be obtained by the expansion 
of the substance; and if it be admitted that 
during the expansion all the intrinsic energy is transformed 
into work, so that at the end the intrinsic energy is zero, it rep- 
resents also the intrinsic energy. In cases for which the equa- 
tion of the adiabatic can be found it is easy to show that 




£1 



pdv 



(24) 



CHANGE OF INTRINSIC ENERGY 



21 



is. a finite quantity; and in any case, if we admit an absolute zero 
of temperature, it is evident that the intrinsic energy cannot 
be infinite. On the other hand, if an isothermal curve were 
treated in the same way the area would be infinite, since heat 
would be continually added during the expansion. 

Now suppose the body to pass from the condition represented 
by A to that represented by B, by any path whatever — that is, 
by any succession of changes whatever — for example, that 
represented by the irregular curve AB. The intrinsic energy 
in the state B is represented by the area VhB^. The change of 
intrinsic energy is represented by the area ^BbaAa, and this 
area does not depend on the form of the curve AB. This graph- 
ical process is only another way of saying that the intrinsic 
energy depends on the state of the substance only, and that 
change of intrinsic energy depends on the final and initial states 
only. 

Another way of representing change of intrinsic energy by 
aid of isodynamic lines avoids an infinite diagram. Suppose 
the change of state to be represented by the 
curve ^^ (Fig. 9). Draw an isodynamic 
line AC through the point A, and an adia- 
batic line BC through B, intersecting at C; 
in general the isoenergic fine is distinct 
from the isothermal line; for example, the 
isothermal line for a saturated vapor is a F1G.9. 

straight line parallel to the OV axis, and 
the isoenergic line is represented approximately by the equation 




pv 



const. 



Then the area ABba represents the external work, and the area 
bBCc represents the change of intrinsic energy; for if the body be 
allowed to expand adiabatically till the intrinsic energy is reduced 
to its original amount at the condition represented by A the 
external work bBCc will be done at the expense of the intrinsic 
energy. 



CHAPTER III. 

SECOND LAW OF THERMODYNAMICS. 

Heat-engines are engines by which heat is transformed into 
work. All actual engines used as motors go through continuous 
cycles of operations, which periodically return things to the 
original conditions. All heat-engines are similar in that they 
receive heat from some source, transform part of it into work, 
and deliver the remainder (minus certain losses) to a refrigerator. 
The source and refrigerator of a condensing steam-engine are 
the furnace and the condenser. The boiler is properly con- 
sidered as a part of the engine, and receives heat from the source. 
Garnet's Engine. — It is convenient to discuss a simple ideal 
engine, first described by Carnot. 

Let P of Fig. lo represent a cyhnder with non-conducting 
walls, in which is fitted a piston, also of non-conducting material, 

and moving without friction; on the 
other hand, the bottom of the cyhnder 
is supposed to be of a material that is 
a perfect conductor. There is a non- 
^ I conducting stand C on which the 
P^^ ^^ cyhnder can be placed while adiabatic 

changes take place. The source of 
heat ^ at a temperature / is supposed to be so maintained 
that in operations during which the cylinder is placed on it, 
and draws heat from it, the temperature is unchanged. The 
refrigerator B at the temperature t^ in like manner can with- 
draw heat from the cylinder, when it is placed on it, at a 
constant temperature. 

Let there be a unit of weight (for example, one pound) of a 
certain substance in the cylinder at the temperature t of the 
source of heat. Place the cylinder on the source of heat A 



CARNOT'S ENGINE 



23 



(Fig. 10), and let the substance expand at the constant tem- 
perature ty receiving heat from the source A. 
If the first condition of the substance be 
represented by A (Fig. 11), then the second 
will be represented by B, and AB will be an 
isothermal. If Ea and Ej, are the intrinsic 
energies at A and B, and if Wab, represented 
by the area aABby be the external work, the 
heat received from A will be 




Fig. 



Q = A {E,-Ea + Wab) (25) 

Now place the cylinder on the stand C (Fig. 10), and let 
the substance expand adiabatically until the temperature is 
reduced to ^1, that of the refrigerator, the change being rep- 
resented by the adiabatic BC (Fig. 11). If E^ is the intrinsic 
energy at C, then, since no heat passes into or out of the 
cylinder', 

= A (E,-E,+ W,,) (26) 

where Wbc is the external work represented by the area bBCc. 
Place the cylinder on the refrigerator B, and compress the sub- 
stance till it passes through the change represented by CD, 
yielding heat to the refrigerator so that the temperature remains 
constant. If Ed is the intrinsic energy at D, then 



-Q^^A(Ea-E,- W,d) 



(27) 



is the heat yielded to the refrigerator, and Wed, represented by 
the area cCDd, is the external work, which has a minus sign, 
since it is done on the substance. 

The point D is determined by drawing an adiabatic from A 
to intersect an isothermal through C. The process is completed 
by compressing the substance while the cylinder is on the stand 
C (Fig. 10) till the temperature rises to /, the change being 
represented by the adiabatic DA. Since there is no transfer 
of heat, 

= A {Ea- Ed- Wda) (28) 



24 SECOND LAW OF THERMODYNAMICS 

Adding together the several equations, member to member, 
Q -Q^^ A (Wa, + W,, - W,a - W,,) . . (29) 

or, if W be the resulting work represented by the area A BCD, 
then 

Q-Q, = AW (30) 

that is, the difference between the heat received and the heat 
delivered to the refrigerator is the heat transformed into work. 

A Reversible Engine is one that may run either in the usual 
manner, transforming heat into work, or reversed, describing 
the same cycle in the opposite direction, and transforming work 
into heat. 

A Reversible Cycle is the cycle of a reversible engine. 

Carnot's engine is reversible, the reversed cycle being 
ADCBA (Fig. 11), during which work is done by the engine 
on the working substance. The engine then draws from the 
refrigerator a certain quantity of heat, it transforms a certain 
quantity of work into heat, and delivers the sum of both to the 
source of heat. 

No actual heat-engine is reversible in the sense just stated, 
for when the order of operations can be reversed, changing the 
engine from a motor into a pump or compressor, the reversed 
cycle differs from the direct cycle. For example, the valve- 
gear of a locomotive may be reversed while the train is running, 
and then the cylinders will draw gases from the smoke-box, 
compress them, and force them into the boiler. The locomotive 
as ordinarily built is seldom reversed in this way, as the hot 
gases from the smoke- box injure the surfaces of the valves and 
cylinders. Some locomotives have been arranged so that the 
exhaust- nozzles can be shut off and steam and water supplied 
to the exhaust-pipe, thus avoiding the damage from hot gases 
when the engine is reversed in this way. Such an engine may 
then have a reversed cycle, drawing steam into the cylinders, 
compressing and forcing it into the boiler; but in any case the 



EFFICIENCY 



25 



reversed cycle differs from the direct cycle, and the engine is 
not properly a reversible engine. 

A Closed Cycle is any cycle in v^hich the final state is the same 
as the initial state. Fig. 12 represents such a 
cycle made up of four curves of any nature 
whatever. If the four curves are of two species 
only, as in the diagram representing the cycle 
of Carnot 's engine, the cycle is said to be simple. 
In general we shall have for a cycle like that of Fig. 12, 




Fig. 12. 



Qa6 + Qbc - Q< 



= A {W\ + W,, 



W 



cd 



W^). 



p 


A 


B 







c 


^ 


-i 


D - 




V 



Fig. 13. 



A closed curve of any form may be consid- 
ered to be the general form of a closed cycle, 
as that in Fig. 13. For such a cycle we have 

j dQ = A I dW, which is one more way of 

stating the first law of thermodynamics. 

It may make this last clearer to consider the cycle of Fig. 14 
composed of the isothermals AB, CD, and EG, and the 
adiabatics BC, DE, and GA. The cycle 
may be divided by drawing the curve 
through from C to F. It is indifferent 
whether the path followed be A BCD EG A 
or ABCFCDEGA, or, again, ABCFGA + 
CDEFC. 

Again, an irregular figure may be 
imagined to be cut into elementary areas by isothermals and 
adiabatic lines, as in Fig. 15. The summation of the areas will 
give the entire area, and the summation of the works represented 
by these will give the entire work represented by the entire area. 

The Efficiency of an engine is the ratio of the heat changed 
into work to the entire heat applied; so that if it be represented 
by e, 

_AW_ -Q' 
"~ Q ' Q 




Fig. 



(31) 



26 SECOND LAW OF THERMODYNAMICS 

for the heat Q' rejected to the refrigerator is what is left after 
AW thermal units have been changed into work. 

Camot's Principle. — It was first pointed 
out by Carnot that the efficiency of a 
reversible engine does not depend on the 
nature of the working substance, but that 
it depends on the temperatures of the 
^ source of heat and the refrigerator. 




Fig. 15. Let us sce what would be the conse- 

quence if this principle were not true. 
Suppose there are two reversible engines R and A^ each taking 
Q thermal units per second from the source of heat, of which 
A is the more efficient, so that 

Q Q -^"^^ 

is larger than 

AW^ _ Q- Q/ 
Q Q ^^^^ 

this can happen only because Qa is less than Q/, for Q is assumed 
to be the same for each engine. Let the engine R be reversed 
and coupled to A, which can run it and still have left the useful 
work Wa — Wr- This useful work cannot come from the 
source of heat, for the engine R when reversed gives to the source 
Q thermal units per second, and A takes the same amount in the 
same time. It must be assumed to come from the refrigerator, 
which receives Qa thermal units per second, and gives up Q/ 
thermal units per second, so that it loses 

(2/ -Qa' = A {Wa - Wr) 

thermal units per second. This equation may be derived from 
equations (32) and (33) by subtraction. 

Now it cannot be proved by direct experiment that such an 
action as that just described is impossible. Again, the first law 
of thermodynamics is scrupulously regarded, and there is no 



SECOND LAW OF THERMODYNAMICS 27 

contradiction or formal absurdity of statement. And yet when 
the consequences of the negation of Carnot's principles are 
clearly set forth they are naturally rejected as improbable, if not 
impossible. The justification of the principle is found in the 
fact that theoretical deductions from it are confirmed by 
experiments. 

Second Law of Thermodynamics. — The formal statement 
of Carnot's principle is known as the second law of thermody- 
namics. Various forms are given by different investigators, 
none of which are entirely satisfactory, for the conception is not 
simple, as is that of the first law. 

The following are some of the statements of the second law: 
(i) All reversible engines working between the same source of 
heat and refrigerator have the same efficiency. 

(2) The efficiency of a reversible engine is independent of the 
working substance. 

(3) ^ self-acting machine cannot convey heat from one body 
to another at a higher temperature. 

The second law is the third general principle of thermody- 
namics; it differs from each of the others and is independent 
of them. Summing up briefly, the first general principle is a 
pure assumption that thermodynamic equations may contain 
only two independent variables; the second is the statement of 
an experimental fact; the third is a choice of one of two 
propositions of a dilemrha. The first and third are justified 
by the results of the applications of the theory of thermo- 
dynamics. 

So far as efficiency is concerned, the second law of thermo- 
dynamics shows that it wotild be a matter of indifference what 
working substance should be chosen; we might use air or steam 
in the same engine and get the same efficiency from either; 
there would, however, be a great difference in the power that 
would be obtained. In order to obtain a diagram of convenient 
size and distinctness, the adiabatics are made much steeper than 
the isothermals in Fig. 11 ; as a matter of fact the diagram drawn 
correctly is so long and attenuated that it would be practically 



a 

V 


b 







28 SECOND LAW OF THERMODYNAMICS 

worthless even if it could be obtained with reasonable approxi- 
mation in practice, as the work of the cycle would hardly over- 
come the friction of the engine. The isothermals for a mixture 
of water and steam are horizontal, and the diagram takes the 
form shown by Fig. 16. In practice a dia- 
gram closely resembhng Carnot's cycle is 
chosen as the ideal, differing mainly in that 
steam is assumed to be supphed and ex- 
hausted. In a particular case an engiiie 
working between the temperatures 362°. 2 F. 
and 158° F. had an actual thermal efficiency of 0.18; the 
ideal cycle had an efficiency of 0.23, and Carnot's cycle had 
an efficiency of 0.25. The ratio of 0.18 to 0.23 is about 0.81, 
which compares favorably with the efficiency of turbine water- 
wheels. 

Carnot's Function. — Carnot 's principle asserts that the 
efficiency of a reversible engine is independent of the nature of 
the working substance; consequently the expression for the 
efficiency will not include such properties of the working sub- 
stance as specific volume and specific pressure. But the prin- 
ciple asserts also that the efficiency depends on the temperatures 
of the source of heat and the refrigerator, which indeed are the 
only properties of the source and refrigerator that can affect 
the working of the engine. 

We may then represent the efficiency as a function of the tem- 
peratures of the source of heat- and the refrigerator, or, what 
amounts to the same thing, as a function of the superior tem- 
perature and the difference of the temperatures, and may write 

AW _ Q -Q' 
e= -Q-- Q = F (t,t-n 

where Q is the heat received, Q^ the heat rejected, and / and /' 
are the temperatures of the source of heat and of the refrigerator 
on any scale whatsoever, absolute or relative. 

If the temperature of the refrigerator approaches near that of 



KELVIN'S GRAPHICAL METHOD 



29 



the source of heat Q — Q' and t — tf become A(3 and A/, and at 
the Hmit dQ and dt, so that 



'f=Fit, dt) 



(34) 



It is convenient to assume that the equation can be expressed 
in the form 

dQ 



Q 



f (t) dt. 



The function/ (/) is known as Carnot's function, and physi- 
cists consider that the isolation of this function and the relation 
of the function to temperature are of great theoretical importance. 

Absolute Scale of Temperature. — It is convenient and cus- 



tomary to assign to Carnot's function the form — 



where T is 



the temperature by the absolute scale referred to on page 3, 
measured from the absolute zero of temperature. This assump- 
tion is justified by the facts that the theory of thermodynamics 
is much simplified thereby, and that the difference between 
such a scale of temperature and the scale of the air-thermometer 
is very small. ^ 

Kelvin's Graphical Method. — This treatment of Carnot 's 
function was first proposed by Lord Kelvin, who illustrated the 
general conception by the following graphical construction: 

In Fig. 17 let ak and bi be two adiabatic lines, and let the 
substance have its condition 
represented by the point a. 
Through a and d draw iso- 
thermal hnes ; then the diagram 
ahcd represents the cycle of a 
simple reversible engine. Draw 
the isothermal line /e, so that 
the area dcef shall be equal to 
abed] then the diagram dcef 
represents the cycle of a reversible engine, doing the same 
amount of work per stroke as that engine whose cycle is repre- 




FiG. 17. 



30 



SECOND LAW OF THERMODYNAMICS 



sented by ahcd; and the difference between the heat drawn 
from the source and deUvered to the refrigerator — i.e., the heat 
transformed into work — is the same. The refrigerator of the 
first engine might serve for the source of heat for the second. 

Suppose that a series of equal areas are cut off by isothermal 
lines, di?>fegh, hgik, etc., and suppose there are a series of reversible 
engines corresponding; then there will be a series of sources of 
heat of determinate temperatures, which may be chosen to 
establish a thermometric scale. In order to have the scale cor- 
respond with those of ordinary thermometers, one of the sources 
of heat must be at the temperature of boiling water, and one at 
that of melting ice; and for the centigrade scale there will be one 
hundred, and for the Fahrenheit scale one hundred and eighty, 
such cycles, with the appropriate sources of heat, between boiling- 
point and freezing-point. To establish the absolute zero of the 
scale the series must be imagined to be continued till the area 
included between an isothermal and the two adiabatics, continued 
indefinitely, shall not be greater than one of the equal areas. 

This conception of the absolute zero 
may be made clearer by taking wide 
intervals of temperature, as on Fig. 
1 8, where the cycle abed is assumed 
to extend between the isothermals of 
o° and ioo° C; that is, fr,om freez- 
ing-point to boiling-point. The 
next cycle, cdef, extends to — ioo° C, 
and the third cycle, efgh, extends 
to — 200° C. The rernaining area, 
which is of infinite_Jength and ex- 
tremely attenuated, is bounded by the 
isothermal gh and the two adiabatics 
ha and g^. The diagram of course 
cannot be completed, and conse- 
quently the area cannot be measured; 
but when the equations to the isothermal and the adiabatics 
are known it can be computed. So computed, the area is found 




Fig. 18. 



SPACING OF ADIABATICS 



31 



to be -^^ of one of the three equal areas ahcd, cdfe, and efhg. 
100 

The absolute zero is consequently 273° C. below freezing-point. 

Further discussion of the absolute scale will be deferred till 

a comparison is made with the air-thermometer. 

Spacing of Adiabatics. — Kelvin 's graphical scale of temper- 
ature is clearly a method of spacing isothermals which depends 
only on our conceptions of thermodynamics and on the funda- 
mental units of weight and length. Evidently the same method 
may be applied to spacing adiabatics, and thereby a new concep- 
tion of great importance may be introduced into the theory of 
thermodynamics. On this conception is based the method for 
solving problems involving adiabatic expansion of steam, as 
will be explained in the discussion of that subject. 

In Fig. 19 let an and do 
be two isothermals, and let 
adj he, Im and no be a series 
of adiabatics, so drawn that 
the areas of the figures ahcd, 
blmc, and Inom are equal; 
then we have a series of 
adiabatics that are spaced in 
the same manner as are the 
isothermals in Figs. 17 and 
18, and, as with those iso- 
thermals, the spacing depends only on our conceptions of ther- 
modynamics and the fundamental units of weight and length. 

In the discussion of Figs. 17 and 18 it was shown that the area 
of the strip between the initial isothermal ab and the two adiabatic 
lines must be treated as finite, and that in consequence the 
graphical process leads to an absolute zero of temperature. On 
the contrary, the area between the adiabatic ad and the two 
isothermals an and do if extended infinitely will bejnfinite, and 
it will be found that there is no lim it to the number of adia- 
batics that can be drawn with the spacing indicated. A like 
result will follow if the isothermals arc extended to the right and 




Fig. 



32 SECOND LAW OF THERMODYNAMICS 

Upward, and if adiabatics are spaced off in the same manner. 
This conclusion comes from the fact pointed out on page 21, 
that the area under an isothermal curve which is extended with- 
out limit is infinite, because heat is continuously supplied, some 
part of which can be changed into work. 

It is convenient to introduce a new function at this 
place which shall express the spacing of adiabatics as 
represented in Fig. 19, and which will be called entropy. 
From what precedes it is evident that entropy has the 
same relations to the adiabatics of Fig. 19 that temperature 
has to the isothermals of Figs. 17 and 18, but that there is this 
radical difference, that while there is a natural absolute zero of 
temperature, there is no zero of entropy. Consequently in prob- 
lems we shall always deal with differences of entropy, and if we 
find it convenient to treat the entropy of a certain condition of a 
given substance as a zero point it is only that we may count up 
and down from that point. 

If the adiabatic line ad in Fig. 19 should be extended to the 
right, it would clearly lie beneath the adiabatic no, which agrees 
with the tacit convention of that figure, i.e., that as spaced the 
adiabatics are to be numbered toward the right and that the 
entropy increases from a toward n. 

The simplest and the most natural definition of entropy from 
the present considerations, is that entropy is that function which 
remains constant for any thange represented by a reversible 
adiabatic expansion (or compression). With this definition in 
view, the adiabatic lines might be called isoentropic lines. It 
should be borne in mind that our present discussion is purposely 
limited to expansion in a non-conducting cylinder closed by a 
piston, or to like operations. More complex operations than 
that just mentioned may require an extension of the conception 
of entropy and lead to fuller definitions. Such extensions of the 
conception of entropy have been found very fruitful in certain 
physical investigations, and many writers on thermodynamics 
for engineers consider that they get like advantages from them. 
There is, however, an advantage in limiting the conception of a 



GRAPHICAL REPRESENTATION OF EFFICIENCY 



33 



new function, however simple that conception may be ; and there 
is an added advantage in being able to return to a simple con- 
ception at will. 

Efficiency of Reversible Engines. — Returning to equation 

(34) and replacing Carnot's function/ (t) by — j as agreed, we 

have for the differential equation of the efficiency of a reversible 
engine 



Q 

or, integrating between limits, 

" Q 



r 









and the efficiency ior the cycle becomes 
Q - 0' T - T 



(35) 



This result might have been obtained before (or without) the 
discussion of Kelvin 's graphical method, and leads to the same 
conclusion, that the absolute temperature can be made to depend 
on the efficiency of Carnot's cycle, and may, therefore, be inde- 
pendent of any thermometric substance. 
As has already been said, this conception 
is more important on the physical side 
than on the engineering side, and its reit- 
eration need not be considered to call for 
any speculation by the student at this time. 

Graphical Representation of Efficiency. 
— Let Fig. 20 represent the cycle of 
a reversible heat-engine. For convenience 
it is supposed there are four degrees of temperature from the 
isothermal AB \o the isothermal DC^ and that there are three 
intervals or units of entropy between the adiabatics AD and 




Fig. 20. 



34 SECOND LAW OF THERMODYNAMICS 

BC. First it will be shown that all the small areas into which 
the cycle is divided by drawing the intervening adiabatics and 
isothermals are equal. Thus we have to begin with a = b and 
a = c by construction. But engines w^orking on the cycles a 
and b have the same efficiency and reject the same amounts 
of heat. These heats rejected are equal to the heats supplied 
to engines w^orking on the cycles c and d, which consequently 
take in the same amounts of heat. But these engines work 
between the same limits of temperature and have the same 
efficiency, and consequently change the same amount of heat 
into work. Therefore the areas c and d are equal. In like 
manner all the small areas are equal, and each represents one 
thermal unit, or 778 foot-pounds of work. 

It is evident that the heat changed into work is represented by 

{T - T') {4.' - <j>), 

and, further, that the same expression would be obtained for a 

similar diagram, whatever number of degrees there might be 

between the isothermals, or intervals of entropy between the 

adiabatics, and that it is not invalidated by using fractions of 

degrees and fractions of units of entropy. It is consequently 

the general expression for the heat changed into work by an 

engine having a reversible cycle. 

It is clear that the work done on such a cycle-ilici-eases as the 

lower temperature T' decreases, and that it is a maximum when 

T^ becomes zero, for which condition all of the heat applied is 

changed into work. Therefore the heat applied is represented 

by 

Q=T (4>'~ <!>), 

and the efficiency of the engine working on the cycle represented 
by Fig. 20 is 

AW _ Q - Q' _ (T -r)(<j>' - cj>) _ T - T 

Q ~ Q ~ T {4>^ -ct>) r ' 

as found by equation (35). The deduction of this equation by 
integration is more simple and direct, but the graphical method 



EXPRESSION FOR ENTROPY 



35 



A 




T 




R 




D 








4>' 

c 




























T' 






Fig. 21 



is interesting and may give the student additional light on this 
subject. 

Temperature-Entropy Diagram. — Thermal diagrams are com- 
monly drawn with pressure and volume for the co-ordinates, 
but for some purposes it is convenient to use other properties 
as co-ordinates, in particular temperature and entropy. For 
exarnple, Fig. 21 represents Carnot's cycle 
drawn with entropies for abscissae and tem- 
peratures for ordinates, with the advantage 
that indefinite extensions „ of the lines are 
avoided, and the areas under consideration 
are' evidently finite and nieasurable. With 
the exception that there appears now to be no 
necessity to show that the areas obtained by subdivision are all 
equal, the discussion for Fig. 20 drawn with pressures and vol- 
umes may be repeated with temperatures and entropies. 

Expression for Entropy. — One advantage of using the tem- 
perature-entropy diagram is that it leads at once to a method 
for computing changes of entropy. Thus in Fig. 22 let AB 
represent an isothermal change, and let Aa 
and Bh be adiabatics drawn to the axis of 0; 
then the diagram ABha may be considered to 
be the cycle for a Carnot's engine working 
between the temperature T and the -absolute 
— zero, and consequently having the efficiency 
unity. The heat changed into work may there- 
fore be represented by 

Q = T {4>' -4>) (36) 

If we are deahng with a change under any other condition 
than constant temperature, we may for an infinitesimal change, 
write the expression 

# = f . . . . . . . . (37) 

and for the entire change may express the change of entropy by 



Fig. 22. 



36 SECOND LAW OF 'THERMODYNAMICS 

which should for any particular case either be integrated 
between limits or else a constant of integration should be 
determined. 

Attention should be called to the fact that the conception of 
the spacing of isothermals and adiabatics is based fundamen- 
tally on Carnot's cycle and the second law of thermodynamics, 
which has been applied only to reversible operations. The 
method of calculating changes of entropy applies in like manner 
to reversible operations; and when entropy is employed for 
calculations of operations that are not reversible, discretion 
must be used to avoid inconsistency and error. 

On the other hand, the entropy of a unit weight of a given 
substance under certain conditions is a perfectly definite quan- 
tity and is independent of the previous history of the substance. 
This may be made evident by the consideration that any point 
on the line no, Fig. 19, page 31, has a certain number of units of 
entropy (for example, three) more than that of any point on 
the adiabatic ad. 

Example. — There may be an advantage in giving a calcu- 
lation of a change of entropy to emphasize the point that it can 
be represented by a number. Let it be required to find the 
change of entropy during an isothermal expansion of one pound 
air from four cubic feet to eight cubic. 

The heat applied may be obtained by integrating the expression 

, , .dO Idv , . p dv 

the value of the latent heat having been taken from page 12. 
From the characteristic equation 

pv = RT 
the above expression may be reduced to 
d<p = [Cp — c„) — " 



APPLICATION TO A REVERSIBLE CYCLE 



37 



or 



(0-2375 — 0.1690) loge - 
4 



0.0475. 




Fig. 23. 



A problem for air is chosen because it can be readily worked 
out at this place; as a matter of fact, there are few occasions in 
practice where there is reason to refer to entropy of air. 

Application to a Reversible Cycle. — A very important result 
is obtained by the application of equation (37) to the calcula- 
tion of entropy during a reversible cycle. In the first place, 
it is clear that the entropy of a substance having its condition 
represented by the point a (Fig. 23), depends on the adiabatic 
line drawn through it; in other words, the entropy depends only 
on the condition of the substance. 
In this regard entropy is like intrin- 
sic energy and differs from external 
work. Suppose now that the sub- 
stance is made to pass through a 
cycle of operations represented by 
the point a tracing the diagram on 
Fig. 23; it is clear that the entropy will be the same at the end 
of the cycle as at the beginning, for the tracing-point will then 
be on the original adiabatic line. As the tracing- point moves 
toward the right from adiabatic to adiabatic the entropy 
increases, and as it moves to the left the entropy decreases, the 
algebraic sum of changes of entropy being zero for the entire 
cycle. This conclusion holds whether the cycle is reversible 
or non-reversible. The cycle represented by Fig. 23 is purposely 
drawn like a steam-engine indicator diagram (which is not 
reversible) to emphasize the fact that the change of entropy is 
zero in any case. 

If the cycle is reversible, then equation (37) may be used for 
calculating the several changes of entropy, and for calculating 
the change for the entire cycle, giving for the cycle 

T 



n 



(38) 



38 SECOND LAW OF THERMODYNAMICS 

This is a very important conclusion from the second law of 
thermodynamics, and is considered to represent that law. The 
second law is frequently applied by using this equation in con- 
nection with a general equation or a characteristic equation, in 
a manner to be explained later. 

Though the discussion just given is simple and complete, 
there is some advantage in showing that equation (38) holds 
for certain simple and complex reversible cycles. 

Thus for Carnot's cycle, represented by Fig. 20, the increase 
of entropy during isothermal expansion is 



^■~*-ff-iP^-4 



T . 

because the temperature is constant. In like manner the 
decrease during isothermal compression is 

so that the change of entropy for the cycle is 

2 _ 2: 

T T 

But from the efficiency of the cycle we have 

Q~ Q' _ T— T . 2! _ Z! • 2 _ 2! _ 

Q " ^ T ' " Q~ T ' " T 7' ~ °' 

A complex cycle like that represented by Fig. 24 may be 
broken up into two simple cycles ABFG 
and CDFE, for each of which individually 
tjie same result will be obtained — that is, 
the increase of entropy from ^ to ^ is 
equal to the decrease from F to G, and 
the increase from C to D is equal to the 




Fig. 24. 

decrease from E to F, so that the sum- 
mation of changes for the entire cycle gives zero. 



MAXIMUM EFFICIENCY 



39 



Fig. 25 represents the simplified ideal diagram of a hot-air 
engine, in which by the aid of a regenerator the adiabatic lines 
of Carnot's cycle are replaced by 
vertical lines without affecting the 
reversibility or the efficiency of the 
cycle. We may replace the actual 
diagram by a series of simple cycles 
made up of isothermals and adia- 
batics, so drawn that the perimeter 
of the complex cycle includes the 
same area and corresponds ap- 
proximately with that of the 
actual diagram. The summation 
for the complex cycle is clearly 
drawing the adiabatic lines near 
make 




Fig. 25. 



of the change of entropy 
zero, as before. But by 
enough together we may 
the perimeter approach that of the actual diagram as 
nearly as we please, and we may therefore conclude that the 
integration for the changes of entropy for that cycle is also zero. 
Maximum Efficiency. — In order that heat may be trans- 
formed into work with the greatest efficiency, all the heat should 
be applied at the highest practicable temperature, and the heat 
rejected should be given up at the lowest practicable tempera- 
ture; this condition is found for Carnot's cycle, which serves 
as the ideal type to which we approach as nearly as practical 
conditions allow. Deviations from the ideal type are of two 
sorts, (i) commonly a different and inferior cycle is chosen as 
being practically more convenient, and (2) the material of 
which the working cylinder is made absorbs heat at high tem- 
perature and gives out heat at low temperature, thus interfering 
with the attainment of the cycle selected. 

The principle just stated must be accepted as immediately 
evident; but there may be an advantage in giving an illustration. 
The complex cycle of Fig. 24 is made up of two simple Carnot 
cycles ABFG and CDEF\ if two thirds of the heat is appHed 
during the isothermal expansion AB Sit 500° C, and one third 
during the expansion CD, at 250° C, and if all the heat is re- 



40 SECOND LAW OF THERMODYNAMICS 

jected at 20° C, the combined efficiency of the diagram may be 
computed to be 

2 ^ 500 - 20 ^ !__ X ^-^^-^^ =0.56; 

3 500 + 273 3 250 + 273 

had the heat been all applied at 500° C, the efficiency would 
have been 

SCO — 20 



0.62. 



500 + 273 



The loss in this case from applying part of the heat at lower 
temperature is, therefore, 

0.62 — o.c;6 

— — = 0.097. 

0.62 

Non-reversible Cycles. — If a process or a cycle is non-rever- 
sible, then the change of entropy cannot be calculated by equa- 
tion (37), and equation (38) will not hold. The entropy will, 
indeed, be the same at the end as at the beginning of the cycle, 

but the integration of -~ for the cycle will not give zero. On 

the contrary, it can be shown that the integration of -~ for the 

entire cycle will give a negative quantity. Thus let the non- 
reversible engine A take the same amount of heat per stroke as 
the reversible engine R which works on Carnot 's cycle, but let 
it have a less efficiency, so that 

P-<^' < a^^ (3,) 

where Q/ represents the heat rejected by the engine A. Then 

Q -Q/ <Q-Q'= {T-T') (^' - <A) . . (40) 

Suppose now that T^ approaches zero and that </>' approaches ^, 
then at the limit we shall have* 

dQi < dQ = Tdcf), 
or 

f^ < #. 



NON-REVERSIBLE CYCLES 41 

Integrating for the entire cycle, we shall have 

where — N represents a negative quantity. The absolute 
value of N will, of course, depend on the efficiency of the non- 
reversible engine. If the efficiency is small compared with that 
of a reversible engine, then the value of N will be large. If 
the efficiency approaches that of a reversible engine, then N 
approaches zero. It is scarcely necessary to point out that N 
cannot be positive, for that would infer that the non-reversible 
engine had a greater efficiency than a reversible engine working 
between the same temperatures. 

Some non-reversible operations, like the flow of gas through 
an orifice, result in the development of kinetic energy of motion. 
In such case the equation representing the distribution of energy 
contains a fourth term K to represent the kinetic energy, and 
equation (15) becomes 

dQ = A (dS + dT + dW + dK) . . .(42) 

As before S represents vibration work, / represents disgregation 
work, and W represents external work. If the vibration and 
disgregation work cannot be separated, then we may write 

dQ = A {dE + dW + dK) (43) 

If a non-reversible process like that just discussed takes place 
in apparatus or appliances that are made of non-conducting 
material, or if the action of the walls on the substance contained 
can be neglected, the operation may properly be called adiabatic ; 
such a use is clearly an extension of the idea stated on page 32, 
and conclusions drawn from adiabatic expansion in a closed 
cylinder cannot be directly extended to this new application. 
Such a non -reversible operation is not likely to be isoen tropic, 
and there is some advantage in drawing a distinction between 
operations which are isoentropic and those which are adiabatic. 



42 SECOND LAW OF THERMODYNAMICS 

A non-reversible operation in non-conducting receptacles may be 
isothermal, or may be with constant intrinsic energy, as will 
appear in the discussion of flow of air in pipes on page 380, and 
the discussion of the steam calorimeter, page 191. Any non- 
reversible process is likely to be accompanied by an increase of 
entropy; this will appear in special cases discussed in the 
chapter on flow of fluids. 

Since the entropy of a pound of a given substance under 
given conditions, reckoned from an arbitrary zero, is a perfectly 
definite numerical quantity, it is possible to determine its entropy 
for any series of conditions, without regard to the method of 
passing from one condition to another. It is, therefore, always 
possible to represent any changes of a fixed weight of a sub- 
stance, by a diagram drawn with temperatures and entropies 
for co-ordinates. If the diagram can be properly interpreted, 
conclusions from it will be valid. It is, however, to be borne in 
mind that thermodynamics is essentially an analytical mathemat- 
ical treatment ; the treatment, so far as it applies to engineering, 
is neither extensive nor difficult. But the student is cautioned 
not to consider that because he has drawn a diagram represent- 
ing a given operation to the eye, he necessarily has a better 
conception of the operation. If any operation involves an 
increase (or decrease) of weight of the substance operated on, 
thermal diagrams are likely to be difficult to devise and liable 
to misinterpretation. 



CHAPTER IV. 

GENERAL THERMODYNAMIC METHOD. 

In the three preceding chapters a discussion has been given 
of the three fundamental principles of thermodynamics, namely, 
(i) the assumption that the properties of any substance can 
be represented by an equation involving three variables; (2) the 
acceptance of the conservation of energy; and (3) the idea of 
Carnot's principle. In the ideal case each of these principles 
should be represented by an equation, and by the combination 
of the three several equations all the relations of the properties 
of a substance should be brought out so that unknown proper- 
ties may be computed from known properties, and in particular 
advantage may be taken of opportunities to calculate such prop- 
erties as cannot be readily determined by direct experiment from 
those which may be determined experimentally with precision. 

Recent experiments have so far changed the condition of 
affairs that there is less occasion than formerly for such a general 
treatment. Of the three classes of substances that are interest- 
ing to engineers, namely, gases, saturated vapors, and super- 
heated vapors, the conditions appear to be as follows. For 
gases there are sufficient experimental data to solve all problems 
without referring to the general method, though the ratio of the 
specific heats is probably best determined by that method. For 
saturated steam there is one property, namely, the specific vol- 
ume, which is computed by aid of the general method, but there 
are experimental determinations of volume which are reliable 
though less extensive. The characteristic equation of super- 
heated steam is now well determined, and the specific heat is 
determined with sufficient precision for engineering purposes, 
so that there is no difficulty in making the customary 
calculations. 

43 



44 GENERAL THERMODYNAMIC METHOD 

The one class of substances for which the necessary properties 
must be computed by aid of the general method, are those vola- 
tile fluids like ammonia and sulphur dioxide, which are used 
for refrigerating machines. 

On the whole, even with conditions as stated, it is desirable 
that the student should master the general thermodynamic 
method, given in this chapter. That method is neither long 
nor hard, and is so commonly accepted that students who have 
mastered it will have no difhculty in reading standard works 
and current literature involving thermodynamic discussions. 
Those cases remaining where the general method or its equiva- 
lent must be used, are best treated by that method, and in the 
case of volatile fluids can be treated only by that method. 

The case having been presented as fairly as possible, dis- 
cretion may be left with the student or his instructor whether 
he shall read the remainder of this chapter before proceeding, 
or whether the chapter shall be altogether omitted. 

The following method of combining the three general prin- 
ciples of thermodynamics, which is due to Lord Kelvin, depends 
on the use of the expression 

BySz BzS V 

as the basis of an operation. This expression is generally used 
as a criterion to determine whether a certain differential is an 
exact differential that can be integrated directly, or whether 
some additional relation must be sought by aid of which the 
expression may be transformed so that it can be integrated. 

Conversely, if we know, from the nature of a given property 
like intrinsic energy, that it can be always calculated for a given 
condition as represented by two variables like temperature and 
volume, then we are justified in concluding that the expression 

8v8t ~ 8t8v ^^^^ 

must be true and that we can use it as the basis of an operation. 



APPLICATION OF THE FIRST LAW 



45 



Now in laying out a general method it is impossible to select 
any particular characteristic equation, and for that reason, if 
no other, the form of the integral equation connecting E with 
/ and V cannot be assigned. But the fact remains that the possi- 
bility of working out any method depends on the assumption of 
the ultimate possibility of writing such an equation, and that 
assumption carries with it the assumption that dE is an exact 
differential. 

Application of the First Law. — The first general principle 
may be taken to be represented by equation (i), 

dQ ^ Cydt + Idv, 

and the first law of thermodynamics by equation (i6), 
dQ = A (dE + dW) = A (dE-h pdv). 

Combining these equations gives 

and comparing with the general form, 

dE =-^ dt -]- -r- dv, 
ot ov 



it is evident that 



^E c, ,Be I ■ 



Now equation (44) is an abbreviated way of writing the 
expression for continued differentiation which may be expanded 
to 

. se . se 

Sv Bt 



46 GENERAL THERMODYNAMIC METHOD 

or replacing the first partial differential coefficients by their 
equivalents, 

■■■-M-mht <«) 

the subscripts being written to avoid possible confusion with 
other partial differential coefficients to be deduced later. 

From the first law of thermodynamics and equation (2) we 
have in like manner 

dQ = A (dE + pdv) = Cpdt + mdp. 

Since the differential dv is inconvenient, we may replace it by 

ov ov 

so that 

dE + p ~ dp + p -~- dtj = Cpdt + mdp. 



Making 


use of the equation 














^87 


'bp 






Sp - 


~ Bi 




gives 




8 

Bp 


&- 




S (m 
' St \a 


-^sp)- 




I /8c; 


\ - 


Bv 


^8V 


I (Bm\ 





.Sp/t St ^ BpSt A\St/p ^ SiSp 



APPLICATION OF THE SECOND LAW 47 

But the assumption of a characteristic equation connecting 
py V, and t carries with it the assumption that 

so that 

3 [©,-(!'),]= I <^') 

Again, from equation (3) we may have 

dQ = A (dE + pdv) = ndp + odv. 

:.dE='^dp+{^j-p)dv (47) 

or, making use of 



Bv^p SpSv 
A\Bv)p~ A \8p)v~~ '• 

■■i[©,-(£)j= '« 

Application of the Second Law. — The second law of thermo- 
dynamics can be expressed by equation (^S), page 37, 



/^=». 



T 



which makes ■— or d<j) an exact differential, so that we may write 
To prepare equation (i) for this transformation, we may write 



48 GENERAL THERMODYNAMIC METHOD 

SO that the preceding equation gives 
Bv 



' T\Bvl 



\t) Bt \t) 



y^2 



or 



Performing a like operation on equation (2) we have 



f-^-^/ + f#, 




Bp \t) Bt \tJ 




'• T\Bp)t T' 




" \Bp)t \Bt)p~ f ' 




juation (3) we have 




f =1^^ + ^^.. 




B /n\ B /o\ 
" By [t/~ Bp \t)' 




-IBr't '•©.- 





r 



(50) 



First and Second Laws Combined. — The result of applying 
both the first and the second laws of thermodynamics to the 



ALTERNATIVE METHOD 49 

equations (i), (2), and (3) may be obtained by combining the 
equations resulting from the appHcation of the laws separately. 
Thus equations (45) and (49) give 



h_ _ I I 

h~ AT 
Equations (46) and (50) give 

jS i^ £ w 

h. " AT 



(52) 



(53) 



And equations (48) and (51) give 

^ = ^("|-'*^) (54) 

It is convenient to transform this last equation by taking 
values of n and from page 12, yielding 

c,-c.=^ATj^ ....... (55) 

The equations deduced in this chapter show the necessary 
relations among the thermal capacities if the laws of thermo- 
dynamics are accepted. Some of them, or equations deduced 
from them, have been used by writers on thermodynamics to 
establish relations or compute properties that cannot be readily 
obtained by direct experiments. 

For the student familiarity with the processes is of more 
importance than any of the results. 

Alternative Method. — Some writers on thermodynamics re- 
serve the discussion of temperature until they are ready to 
define or assume an absolute scale independent of any substance 
and depending only on the fundamental units of length and 
weight. Of the three general equations (i), (2), and (3) they 
use at first only the latter: 

dQ = ndp + odv. 



50 



GENERAL THERMODYNAMIC METHOD 



Now from equation (i6), representing the first law of thermo- 
dynamics, 

dQ = A (dE + pdv), 

it is evident that dQ is not an exact differential, since the equa- 
tion cannot be integrated directly. The fact that in certain 
cases p may be expressed as a function of Vy and the integral 
for external work can be deduced, does not affect this general 
statement. Suppose that there is some integrating factor, 

which may be represented by — , so that 

IQ^ldp + ^dv 
s s ^ s 

may be integrated directly; we may then consider that we have 
a series of thermal lines represented by making 

•- = const., — = const., — = const., etc. 

o o o 

These lines with a series of adiabatic lines represented by 
(j) = const., (j>^ = const., ^'' = const., etc., 

allow us to draw a simple cycle of operations represented by Fig. 
25a, in which AB and CD are represented by the equations 

I = C, and ^ = C, 

Is while AD and BC are adiabatics. The effi- 
b le V ciency of a reversible engine receiving the 
Fig. 2sa. Yieat Q during the operation AB, and reject- 

ing the heat Q' during the operation CD, will be 

Q-Q' AW 



But -^ is an exact differential, and depends on the state of 




ZEUNER'S EQUATIONS 51 

the substance only, and consequently is the same at the end as 
at the beginning of the cycle, so that for the entire cycle 

V(3 



/f 



Now during the operations represented by the adiabatics AD 
and BC no heat is transmitted, and during the operations rep- 
resented by the lines AB and CDj --is constant; consequently 
the integration of the above equation for the cycle gives 

Q G' 

— — -^^ = o. 

S S' 

. Q -Q' _ s - s\ 

" Q S ' 

that is, the efficiency of an engine v^orking on such a cycle depends 
on 5 and 5', and on nothing else. 

Zeuner's Equations. — A special form of thermodynamic 
equations has been developed by Zeuner and through his influ- 
ence has been impressed to a large extent on German writings. 
These equations can be deduced from those already given in 
the following manner. 

From the application of the first law of thermodynamics to 
equation (3) we have equation (47), page 47, 





dE -- 


=>- 


Ki- 


-.) 


dv. 


Now 


dE - 


■1^' 


^g 


dv. 




so that 














n 
A ~ 


- Bp' 




A ~ 


SE 

' Sv 


+ P 


These properti 


as Zeuner writes 








X = 




Y = 


P + 


SE 
Sv- 



52 GENERAL THERMODYNAMIC METHOD 



Solving equation (54) 


first for and then for 


n. 




AT + 








AT-, 

- « = ;- 


Bt 





^^, 

In equation (3) 

dQ = ndp + odVj 

we may substitute the above ^values successively giving 
dQ = ^ In ^ dp -}- n J- dv + A Tdv] • 

/. dQ ^ ^ indt + ATdvj 

hp 

hi h , 

because dt = ^— dp + r— a^' • 

op ov 

And also 

dQ='^{o^^dp^olLdv--ATdp). 



',dQ = ^(odt ~ ATdp]' 



hv 

Replacing and n by their values in terms of X and F, 
dQ =A (Xdp + Ydv), 

dQ=jJ^Xdl+ (^4-/) ^4 

Tp 

dQ = f^[Ydt + {l + t)dp]. 



ZEUNER'S EQUATIONS 53 

In these equations a is tlie coefficient of dilatation, or — h / is 
equal to T, and 

If this derivation of Zeuner's equations is borne in mind, the 
treatment of thermodynamics by many German writers may be 
readily recognized to be only a variant on that developed by 
Clausius and Kelvin. 



CHAPTER V. 

PERFECT GASES. 

The characteristic equation for a perfect gas is derived from 
a combination of the laws of Boyle and Gay-Lussac, which 
may be stated as follows: 

Boyle's Law. — When a given weight of a perfect gas is com- 
pressed (or expanded) at a constant temperature the product 
of the pressure and the volume is a constant. This law is nearly 
true at ordinary temperatures and pressures for such gases as 
oxygen, hydrogen, and nitrogen. Gases which are readily 
liquefied by pressure at ordinary temperatures, such as ammonia 
and carbonic acid, show a notable deviation from this law. The 
law may be expressed by the equation 

pv = p,v, . . • (56) 

in which p^ and v^ are the initial pressure and volume; p is any 
pressure and v is the corresponding volume. 

Gay-Lussac's Law. — It was found by Gay-Lussac that any 
volume of gas at freezing-point increases about 0.003665 of its 
volume for each degree rise of temperature. Gases which are 
easily liquefied deviate from this law as well as from Boyle's 
law. In the deduction of this law temperatures were measured 
on or referred to the air-thermometer, and the law therefore 
asserts that the expansibility or the coefficient of dilatation of 
perfect gases is the same as that of air. Gay-Lussac 's law may 
be expressed by the equation 

V = v^{i + at) . (57) 

in which t^o is the original volume at freezing-point, a is the 
coefficient of dilatation or the increase of volume for one degree 
rise of temperature, and v is the volume corresponding to the 
temperature t measured from freezing-point. 

54 



CHARACTERISTIC EQUATION 55 

Characteristic Equation. — From equation (57) we may 
calculate any special volume, such as v^, getting 

^'l = Vq (1 + at). 

Assuming that p^ in equation (56) is the normal pressure of 
the atmosphere pQ, and substituting the value just found for Vj^, 
we have for the combination of the laws of Boyle and Gay- 
Lussac 

pv =poVo (i + at) =poVoa (^ + ^ j • • • • (5^) 

If it be assumed that a gas contracts a part of its volume at 
freezing-point for each degree of temperature below freezing 

then the absolute zero of the air-thermometer will be — degrees 
below freezing, and 

a 

may be replaced by T, the absolute temperature by the air- 
thermometer. 

The usual form of the characteristic equation for perfect 
gases may be derived from equation (58) by substituting Tq, 

the absolute temperature of freezing-point, for - , giving 



p = ^T=RT (59) 

^ 



where i? is a constant representing the quantity 



0^0 

T 
^ 



For solution of examples it is more convenient to write equa- 
tion (59) in the form 

^=^ (60) 



56 PERFECT GASES 

Absolute Temperature. — Recent investigations of the prop- 
erties of hydrogen by Professor Callender * indicate that the 
absolute zero is 273°.! C. below freezing-point. This does 
not differ much from taking a = 0.003665 as given by Regnault, 
for v^^hich the reciprocal is 272.8. In this w^ork we shall take 
for the absolute temperature 

r = / + 273° centigrade scale. 
r = ^ + 459°.5 Fahrenheit scale. 

These figures are convenient and sufficiently exact. 

Relation of French and English Units. — For the purpose of 
conversion of units from the metric system (or vice versa) the 
following values may be used: 

one metre = 39.37 inches, 
one kilogram = 2.2046 pounds. 

Specific Pressure. — The normal pressure of the atmosphere . 
is assumed to be equivalent to that of a column of mercury, 
760 mm. high at freezing-point. Now Regnault t gives for 
the weight of a litre, or one cubic decimetre, of mercury 13.5959 
kilograms; consequently the specific, pressure of the atmosphere 
under normal conditions is 

p^ = 10,333 kilograms per square metre. 

Using the conversion units given above for reducing this 
specific pressure to the English system of units gives 

po = 2116.32 pounds per square foot, 

which corresponds to 

14.697 pounds per square inch, 
or to 

29.921 inches of mercury. 

It is customary and sufficient to use for the pressure of the 
atmosphere 14.7 pounds to the square inch. 

* Phil. Mag., Jan., 1903. 

t Memoir es de PInstitni.de France, vol. xxi. 



SPECIFIC VOLUMES 



57 



Specific Volumes of Gases. — From recent determinations of 
densities of gases by Leduc, Morley, and Raleigh it appears that 
the most probable values of the specific volume of the commoner 
gases are 

VOLUMES IN CUBIC METRES OF ONE KILOGRAM. 

Atmospheric air ...,.„..,.,.. 0.7733 

Nitrogen 0.7955 

Oxygen ....,..,..,...,. 0.6996 

Hydrogen .-..'.,.„. 11.123 

The corresponding quantities for English units are given in 
the next table: 

VOLUMES IN CUBIC FEET OF ONE POUND. 

Atmospheric air . . » . „ 12.39 

Nitrogen , , , . , . . 12.74 

Oxygen 12.21 

Hydrogen 178.2 

To these may be added the value for carbon dioxide, 0.506 
cubic metre per kilogram or 8.10 cubic feet per pound; but 
as the critical temperature for this substance is about 31° C, or 
88° F., calculations by the equations for gases are liable to be 
affected by large errors. 

Value of R. — The constant R which appears in the usual 
form of the characteristic equation for a gas represents the 
expression 

To ' 
The values for R corresponding to the French and the English 
system of units may be calculated as follows: 

French units, R = ^^^^-^ ^ ^'^^^^ = 29.27 . . (61) 

273 

T- T 1. •. 7-» 2116.^ X 12.^0 ,. X 

English units, R = ^ ^ = 53.35 . . (62) 

491-5 

\^alue of R for other gases may be calculated in a like manner. 



58 PERFECT GASES 

Solution of Problems. — Many problems involving the proper- 
ties of air or other gases may be solved by the characteristic 
equation 

pv = RT, ' 



or by the equivalent equation 



T To 



which for general use is the more convenient. 

In the first of these two equations the specific pressure and 
volume to be used for EngHsh measures are pounds per square 
foot, and the volume in- cubic feet of one pound. 

For example, let it be required to find the volume of 3 pounds 
of air at 60 pounds gauge-pressure and at 100° F. Assuming a 
barometric pressure of 14.7 pounds per square inch, 

V = ^^ ^^ ^^^^ ^ = 2.774 cubic feet 

(14.7 +,60)144 

is the volume of i pound of air under the given conditions, and 
3 pounds will have a volume of 

3 X 2.774 = 8.322 cubic feet. 

The second equation has the advantage that any units may 
be used, and that it need not be restricted to one unit of weight. 

For example, let the volume of a given weight of gas, at 100° C. 
and at atmospheric pressure, be 2 cubic yards; required the 
volume at 200° C. and at 10 atmospheres. Here 

10 V _ 1X2 

473 373 ' • 

V = -^-^ = 0.2 1; ^6 cubic yards. 

10 X 373 ^^ ^ 

Specific Heat at Constant Pressure. — The specific heat for 
true gases is very nearly constant, and may be considered to be 



APPLICATION OF LAWS OF THERMODYNAMICS 59 

SO for thermodynamic equations. Regnault gives for the mean 
values for specific heat at constant pressure the following results : 

Atmospheric air ............. 0.2375 

Nitrogen 0.2438 

Oxygen 0.2175 

Hydrogen 3 . 409 

Ratio of the Specific Heats. — By a special experiment oh 
the adiabatic expansion of air, Rontgen* determined for the 
ratio of the specific heats of air, at constant pressure and at 
constant volume, 

tc = ■£■= 1.405. 

This value agrees well with a computation to follow, which 
depends on the application of the laws of thermodynamics to a 
perfect gas, and also with a determination from the theory of 
gases by Lovef that the ratio for air should be 1.403. If the 
given value for this ratio be accepted the remainder of the work 
in this chapter follows without any reference to the laws of 
thermodynamics . 

Application of the Laws of Thermodynamics. — The preced- 
ing statements concerning the specific heats of perfect gases 
and their ratio would be satisfactory were it definitely determined 
by experiment that the specific heat at constant volume is as 
nearly constant as is the specific heat at constant pressure. 
None of the experimental determinations (not even that by Joly %) 
can be considered as satisfactory as those for the specific heat 
at constant pressure; consequently there is considerable impor- 
tance to be attached to the application of the laws of thermo- 
dynamics to the characteristic equation for a perfect ga;s, and, 
moreover, this application furnishes one of the most satisfactory 
determinations of the ratio of the specific heats. 

* Poggendorff's Annalen, vol. cxlviii, p. 580. 

t Phil. Mag., July, 1899. 

t Proc. Royal Soc, vol. xli, p. 352, 1886. 



6o PERFECT GASES 

It is convenient at this place to make the appHcation of the 
laws of thermodynamics by aid of equation (55), page 49. 



From the equation 
we have 



Cp- c. 


= AT 


, I 
8tBt° 






8v Sp 


pv = 


RT, 




3/ 


p St 
R'Sp 


V 

^ r' 


.-. Cp 


— c, = 


= AR 



(63) 



(64) 



This equation shows conclusively that if the characteristic 
equation is accepted the differences of the specific heats must be 
considered to be constant, and if one is treated as constant so 
also must the other. Conversely, the assumption of constant 
specific heats for any substance is in effect the assumption of 
the characteristic equation for a perfect gas. 

The solution of equation (64) for the ratio of the specific 
heats gives 



f. AR 



ic= = 1.406. 

J _ 10333 X 0'7733 
426.9 X 273 X 0.2375 

For those who have not read Chapter IV, the following deriva- 
tion of equation (64) may be interesting. In Fig. 26 let ah repre- 
sent the change of volume at constant pressure due 
to the addition of heat c^A/ where A/ is the increase 
of temperature ; and let cb represent the change of 
V pressure due to the addition of heat c^A/; if ac is 



Fig. 26. ^n isothermal, the latter change of temperature will 
be equal to the former, but the heat applied will be less on account 
of the external work pi^v (approximtely). Consequently, 

Cp — c,^ Ap ^ = AR, 



ISOTHERMAL LINE 6l 

the last transformation making use of the partial derivative 

S/ " p 

Thermal Capacities. — The values of the several thermal 
capacities for a perfect gas were derived on page 12 and may be 
written 

I = ^ (Cp - c,,) = - (Cp — c^) . . e . (66) 

K V 



-(c,-c„)=-- 



^^ — l^{(^P~^v) =— - (Cp — C^) . . (67) 



w = - Cr = 7 c« . (68) 

K p 

=^Cp= ■- Cp ........ (69) 

K v 

the transformations in equations (66) and (67) being made by 
aid of the characteristic equation. 

General Equations. — To deduce the general equations for 
gases from equations (i), (2), and (3), it is only necessary to 
replace the letters /, m, n, and by their values just obtained, 
giving 

T 
dQ =- cjt + (Cp — c^) - dv (70) 

"^ 

T 

dQ = Cpdt -r (c^ — Cp)-- dp . . : . . (71) 

P 

T T 
dQ == c^ - dp + Cp - dv (72) 

p V 

Isothermal Line. — The equation to the isothermal Hne for 
a gas is obtained by making T a constant in the characteristic 
equation, so that 

pv =^ RT^ = p,v„ 
or 

pv = p,v^ ...... (73) 

This equation will be recognized as the expression of Boyle's 
law. It is, of course, the equation to an equilateral hyperbola*. 



62" PERFECT GASES 

To obtain the external work during an isothermal expansion 
we may substitute for p in the expression 



W 



Jpd^. 



from the equation to the isothermal line just stated, using for 
limits the final and initial volumes, V2 and z\j 



W 



^ ^1^^ A "^7 = ^1^1 ^^^' ~ • • ' • (74) 



If the problem in any case calls for the external work of one 
unit of weight of a gas, then v^ and V2 must be the initial and 
final specific volumes; but in many cases the initial and final 
volumes are given without any reference to a weight, and it is 
then sufficient to find the external work for the given expansion 
from the initial to the final volume without considering whether 
or not they are specific volumes. 

The pressures must always be specific pressures ; in the English 
system the pressures must be expressed in pounds on the square 
foot before using them in the equation for external work, or, for 
that matter, in any thermodynamic equation. 

For example, the specific volume of air at freezing-point and 
at 14.7 pounds pressure per square inch is about 12.4 cubic feet; 
at the same temperature and at 29.4 pounds per square inch the 
specific volume is 6.2 cubic feet. The external work during 
an isothermal expansion of one pound of air from 6.2 to 12.4 
cubic feet is 



PI - p^v, I — = p,v, log, - 



124 
= 29.4 X 144 X 6.2 loge -~ =18,190 foot-pounds. 

6.2 

For example, the external work of isothermal expansion from 
3 cubic feet and 60 pounds pressure by the gauge to a volume 
of 7 cubic feet is 

W =■■ (60 + 14.7) 144 X 3 logg^ = 27,340 foot-pounds. 

3 



ISOENERGIC LINE 63 

In both problems the pressure per square inch is multipHed 
by 144 to reduce it to the square foot. In the first problem the 
pressures are absolute, that is, they are measured from zero 
pressure; in the second problem the pressure by the gauge is 
60 pounds above the pressure of the atmosphere, which is here 
assumed to be 14.7 pounds per square inch, and is added to 
give the absolute pressure. In careful experimental work the 
pressure of the atmosphere is measured by a barometer and is 
added to the gauge-pressure. 

Isoenergic Line. — The isothermal line for a perfect gas is 
also the isoenergic line, a fact that may be proved as follows : 
The heat applied during an isothermal expansion may be cal- 
culated by making T a constant in equation (70) and then 
integrating; thus: 

^1 V v., 

or, substituting for c^ — c„ from equation (64), 

Q = ART, log,^ = Ap,v, log, J . . . (75) 

A comparison of equation (75) with equation (74) shows 
that the heat applied during an isothermal expansion is equiv- 
alent to the external work, or we may say that all the heat applied 
is changed into external work, so that the intrinsic energy is not 
changed. This conclusion is based on the assumption that 
the properties are accurately represented by the characteristic 
equation and that the specific heats are constant. As both 
assumptions are approximate so also is the conclusion, as will 
appear in the discussion of flow through a porous plug. 

An interesting corollary of the discussion just given is that 
an infinite isotherftial expansion gives an infinite amount of 
work. Thus the area contained between the 
axis OV (Fig. 27), the ordinate ah, and the 
isothermal line aa extended without limit is 



W = p,v^ log, — - ^^ . 



\ 






Fig. 27. 



64 PERFECT GASES 

This may also be seen from the consideration that if heat be 
continually applied, and all changed into work, there will be a 
hmitless supply of work. 

Adiabatic Lin«s. — During an adiabatic change — for exam- 
ple, the expansion of a gas in a non-conducting cylinder — heat 
is not communicated to, nor abstracted from, the gas; conse- 
quently dQ in equations (70), (71), and (72) becomes zero. 

From equation (72) 

T T 

o = dQ = c„ — dp + Cp — dv; 

p V 

^dv __ _ dp 

*' c^ V p ' 



'-(#-'*(?)■ 



The ratio — of the specific heats may be represented by ^c, and 
the above equation may be written 

(76) 

v^p = v^^pi = const (77) 






This is the adiabatic equation for a perfect gas which is most 
frequently used. If adiabatic equations involving other varia- 
bles, such as^i and Tj, are desired, they may be derived from 
equation (76) by aid of the characteristic equation, which for 
this purpose may be written 

pv _ pjV^ 

T ~ t/ 

so that £1 _ vT^ 

p" v,t' 

Q'-^i--. ..... :.m 

/. Tv^-^ = T.vr'' (79) 



ADIABATIC LINES 



65 



Or equations (78) and (79) may be deduced directly from 
equation (70) as equations (76) and (77) were from equation 

(72). 

In like manner we may deduce from equation (71) 

l-K l-K 

Tp ' = T,p, ^ (80) 

or we may derive it from equation (76). 
To find the external work the equation 



W = 



/ pdv 



may be used after substituting for p from equation (77) 



W 






In Fig. 28 the area between the axis OV, p 
the ordinate ba, and the adiabatic line aa ex- 
tended without limit, becomes 



W, 



AC — I 



\, 



Fig. 28. 



and not infinity, as is the case with the isothermal line. 

Here, as with the calculation of external work during iso- 
thermal expansion, specific volumes should be used when the 
problem involves a unit of weight; but work may be calculated 
for any given initial and final volumes without considering 
whether they are specific volumes or not. The pressures are 
always pounds on the square foot for the English system. 

For example, the external work of adiabatic expansion from 
3 cubic feet and 60 pounds pressure by the gauge to the volume 
of 7 cubic feet is 



W 



^ 74-7 X^i44 X 3 I ^ _ ^ly-- j ^ ^3^^^^ foot-pounds, 



66 PERFECT GASES 

which is considerably less than the work for the corresponding 
isothermal expansion. 

Attention should be called to the fact that calculations by this 
method are subject to a considerable error from the fact that 
the denominator of the coefficient contains the term /c — i equal 
to 0.405 ; if it be admitted that the last figure is uncertain to the 
extent of two units, the error of calculation becomes half a per 
cent. 

Intrinsic Energy. — Since external work during an adiabatic 
expansion is done at the expense of the intrinsic energy, the work 
obtainable by an infinite expansion cannot be greater than the 
intrinsic energy. If it be admitted that such an expansion 
changes all of the intrinsic energy into external work we shall 
have 

E,^W, = -^^ (82) 

fc — 1 

which gives a ready way of calculating intrinsic energy. In 
practice we always deal with differences of intrinsic energy, so 
that even if there be a residual intrinsic energy after an infinite 
adiabatic expansion the error of our method will be eliminated 
from an equation having the form 

E,-E,= 1^--^ ..... (83) 

Exponential Equation. — The expansions and compressions 
of air and other gases in practice are seldom exactly isothermal or 
adiabatic; more commonly an actual operation is intermediate 
between the two. It is convenient and usually sufficient to 
represent such expansions by an exponential equation, 

pv"" = p,v,- (84) 

in which n has a value between unity and 1.405. The form of 
integration, for external work is the same as for that of adiabatic 
expansion, and the amount of external work is intermediate 
between that for adiabatic and that for isothermal expansion. 



ENTROPY 



67 



Change of temperature during such an expansion may be 
calculated by the equations 

T,v--' ....... (85) 



Tp ^ 



l-n 



(86) 

which may be deduced from equation (84) by aid of the char- 
acteristic equation ^ „„ 
^ pv = RT 

as equation (79) is deduced from equation (76). 

If it is desired to find the exponent of an equation representing 
a curve passing through two points, as a^ and 6^2 
(Fig. 29), we may proceed by taking logarithms 
of both sides of the equation 

giving 



o 7. 



so that 



n log v^ +log p^ = n log v^ + log p^, 
los: p^ — log p^ 



Fig. 29. 



n = :-— r— (87) 

log V, - log V, 

For example, the exponent of an equation to a curve passing 
through the points 

Pi = 74-7. "^1 = 3y and p^ = 30, v^ = 7, 

is log 74.7 — log so 

n = 7 ^^ ^ , ^ ^ = 1. 104. 

log 7 — log 3 

It should be noted that as n approaches unity the probable 

error of calculation of external work is liable to be very large. 

Entropy. — For anv reversible process 

- ' # = f; 



consequently from equations (70), (71), and (72) we have 
d(t> 



dt , . 



. dv 

Cv) > 

V 



d(t> 



dt 



(^p-i^ + {^v — Cp) -f ' 

T p 



d<p = c^ -j- + Cp — ; 
p V 



68 PERFECT GASES 

and, integrating between limits, 

</>,-(/>, = c, log,^ + {c^ - c,) log, -^ . . (88) 

*2 - *i = Cp loge =r- + (S - (^v) log, ^' . . (89) 

J- 1 ^2 

j) V 

^■l — ^l- Cv loge r + ^P log« -"•••• (90) 



Pi -- - V 



which give ready means of calculating changes of entropy. 
These equations give the entropy changes per pound, and are to 
be multiplied by the weight in pounds to give the change for 
the actual conditions. 

For example^ the change of entropy in passing from the pres- 
sure of 74.7 pounds absolute per square inch and the volume 
of 3 cubic feet to the pressure of 30 pounds absolute and the 
volume of 7 cubic feet is 

<f>2 — <Pi = — ^^ loge -"^— + 0.2375 loge - = 0.0454. 
1.405 74.7 3 

Since the pressures form the numerator and denominator of 
a fraction, there is no necessity to reduce them to the square 
foot. In this problem the pressures and volumes are taken at 
random; they correspond to a temperature of 146° F., at the 
initial condition. As has already been said, there is seldom 
occasion in practice for using the entropy of a gas. 

Comparison of the Air-Thermometer with the Absolute Scale. 
— In connection with the isodynamic line it was shown that the 
intrinsic energy is a function of the temperature only. This 
conclusion is deduced from the characteristic equation on the 
assumption that the scale of the air-thermometer coincides with 
the thermodynamic scale, and it affords a delicate method of 
testing the truth of the characteristic equation, and of comparing 
the two scales. 



COMPARISON OF THE AIR THERMOMETER 69 

The most complete experiments for this purpose were made 
by Joule and Lord Kelvin, who forced air slowly through a porous 
plug in a tube in such a manner that no heat was transmitted 
to or from the air during the process. Also the velocity both 
before and beyond the plug was so small that the work due to 
the change of velocity could be disregarded. All the work that 
would be developed in free expansion from the higher to the 
lower pressure was used in overcoming the resistance of friction 
in the plug, and so converted into heat, and as none of this heat 
escaped it was retained by the air itself, the plug remaining at a 
constant temperature. It therefore appears that the intrinsic 
energy remained the same, and that a change of temperature 
indicated a de^dation from the assumptions of the theory of 
perfect gases. 

In the discussion of results given by Joule and Lord Kelvin* 
in 1854 they gave for the absolute temperature of freezing-point 
273°. 7 C. As the result of later experiments t they stated that 
the cooling for a difference of pressure of 100 inches of mercury 
was represented on the centigrade scale by 



o.°93 {^) 



' From these experiments and from other considerations con- 
cerning the constant-volume hydrogen thermometer. Professor 
Callendar has determined that the most probable value for the 
absolute temperature of freezing-point is 273°.! C, as already 
given, and gives a table of corrections to the hydrogen ther- 
mometer to obtain temperatures on the absolute scale. As 
the correction at any temperature between — 200° and + 450° 
C. is not more than t^tf of a degree this is interesting mainly 
to physicists. The corrections for the air-thermometer at con- 
stant pressure are somewhat larger, but approach tV of a degree 
only at 300° C. 

* Phil. Trans, vol. cxliv, p. 349, 
t Ihid. vol. clii, p. 579. 



70 



PERFECT GASES 



Deviation from Boyle's Law. — Early experiments on the 
permanent gases (as they were then known) indicated that 
there were small deviations evident to a physicist, but not of 
importance to engineers; but now that air is compressed to 
pressures as high as 2500 pounds per square inch, it becomes 
necessary to take account of such deviations in engineering 
practice. 

Perhaps the best conception of this subject, and of the four 
recognized states of fluids, can be had from a consideration of 
Andrews' * experiments, which for the present purpose are con- 
veniently represented by his isothermal curves, which are repro- 
duced in Fig. 29a, together with the curves for air. The latter 
are approximate hyperbolae referred to the proper axes, that 
for zero pressure being nearly the whole height of the diagram 
below the figure as it is drawn. At 48°.! C, the isothermal for 
carbonic acid shows a marked deviation from the hyperbola, as 
may be seen by comparison with the curves for air, or better 
from the fact that a rectangular hyperbola through P will pass 
through Q. On the other hand, the isothermal for 13°.! resem- 
bles that for steam, which is commonly known as a saturated 
vapor whose pressure is constant at constant 
temperature; the horizontal part of this line 
represents a mixture of liquid and vapor 
which at the left runs into the liquid curve, 
and as liquid carbonic acid has considerable 
compressibility, this curve becomes a straight 
line with an appreciable inclination to the 
axis of zero volume. At the right, the iso- 
thermal shows a decided break and slopes 
away as the volume becomes larger than 
that of the saturated vapor. The isothermal 
for 21°. 5 shows similar characteristics, but 
the passages from one condition to another are more gradual. 
The dotted curve is drawn through the points of saturation and 
liquefaction, and its crest corresponds to the critical temperature. 

* Phil. Trans., 1869, part ii, p. 575, and 1876, part ii, p. 421. 



LOO- 
95- 

90- 
85- 
80 
ffS- 
70' 
6S 
60 
'55- 




Fig. 29a. 



DENSITY AT HIGH PRESSURE 71 

The isothermal for 31.°! is clearly above the critical tempera- 
ture and does not indicate a liquefaction. 

The several states of a fluid may be enumerated as 

1 . Liquid. 

2. Saturated vapor, including mixtures of liquid and vapor. 

3. Superheated vapor characterized by a larger volume than 

saturated vapor for a given temperature and pressure. 

4. Gas; near the critical temperature the deviations from 

Boyle's law are very large, at higher temperature the 
deviations diminish and become unimportant. 
Critical Temperatures. — The foUov^ing table of critical 
temperatures and of boiling-points at atmospheric pressure is 
taken in part from Preston's " Theory of Heat," 1904. 

Boiling-Point. Critical Temperature. 

Hydrogen . -252.^7 C. -234.°5 C. 

Nitrogen —194.4 —146 

Oxygen —182.2 — 118.8 

Air —1 91. 4 —140 

Carbon monoxide ....... — 190 —139.5 

Carbon dioxide —78.3 +31 -35 

Sulphur dioxide —10 -hi 57.0 

Ether 34.5 175 

Alcohol 78.4 248 

Carbon bisulphide 43.3 254 

Water 100 362 

Density at High Pressure. — If the usual methods (given on 
page 58) for the solution of problems involving the properties 
of gases, are applied v^ith very high pressure, errors amounting 
to two or three per cent are liable to be incurred, owing to the 
deviation from Boyle's law. In some cases, this error may be 
ignored in engineering practice; in some cases the error may be 
included in a practical factor, as will be indicated in the design of 
air compressors; and in other cases allowances must be made 
from the experimental information furnished by Armagat, and 
which may be found in Landolt and Bornstein's Tables. 



72 



PERFECT GASES 



Rontgen's Experiments. — Direct experiments to determine 
K may be made as follows. Suppose that a vessel is filled with 
air at a pressure p^, while the pressure of the atmosphere is pa. 
Let a communication be opened with the atmosphere sufficient 
to suddenly equalize the pressure; then let it be closed, and let 
the pressure p^ be observed after the air has again attained the 
temperature of the atmosphere. If the first operation is suffi- 
ciently rapid it may be assumed to be adiabatic, and we may 
use equation (77), from which 

^^ \ogp,-\ogPa 

log Va - log V^ 

The second operation is at constant volume; consequently 
the specific volume is the same at the final state as after the 
adiabatic expansion of the first operation. But the initial and 
final temperatures are the same; consequently 

.-. log v^ — log V, = log Pi — log />2, 
which substituted in equation (91) gives 

^ ^ log^^-logi, 

log p, - log p, ^^ ^ 

The same experiment may be made by rarefying the air in 
the vessel, in which case the sign of the second term changes. 

Rbntgen* employed this method, using a vessel containing 
70 htres, and measuring the pressure with a gauge made on 
the same principle as the aneroid barometer. Instead of assum- 
ing the pressure pa at the instant of closing the stop- cock to be 
that of the atmosphere, he measured it with the same instrument. 
A mean of ten experiments on air gave 

/c = 1.4053. 

* Poggendorff's Annalin, vol. cxlviii, p. 580. 



EXAMPLES 73 



EXAMPLES. 



1. Find the weight of 4 cubic metres of hydrogen at 30° C, 
and under the pressure of 800 mm. of mercury. Ans. 0.341 kg. 

2. Find the volume of 3 pounds of nitrogen at a pressure of 
45 pounds to the square inch by the gauge and at 80° F. Ans. 
11.05. 

3. Find the temperature at which one kilogram of air will 
occupy one cubic metre when at a pressure of 20,000 kilograms 
per square metre. Ans. 410° C. 

4. Oxygen and hydrogen are. to be stored in tanks 10 inches 
in diameter and 35 inches long. At a maximum temperature 
of 110° F., the pressure must not exceed 250 pounds gauge. 
What weight of oxygen can be stored in one tank? What of 
hydrogen? Ans. Oxygen 2.21 pounds. Hydrogen 0.138 pound. 

5. A balloon of 12,000 cubic feet capacity, weighing with car, 
occupant, etc., 665 pounds, is inflated with 9500 cubic feet 
hydrogen at 60° F., the barometer reading 30 inches. Find 
the weight of the hydrogen and the pull on the anchor rope; 
find also the amount that the balloon must be lightened to reach 
a height where the barometer reads 20 inches, and the tempera- 
ture is 10° below zero Fahrenheit. Ans. Weight hydrogen 
50.4 pounds; pull on rope 12 pounds; balloon lightened 7.5 
pounds. 

6. A gas-receiver holds 14 ounces of nitrogen at 20° C, and 
under a pressure of 29.6 inches of mercury. How many will it 
hold at 32° F., and at the normal pressure of 760 mm.? Ans. 
15.18 ounces. 

7. A gas- receiver having the volume of 3 cubic feet contains 
half a pound of oxygen at 70° F. What is the pressure ? Ans. 
29.6 pounds per square inch. 

8. Two cubic feet of air expand at 50° F. from a pressure 
of 80 pounds to a pressure of 60 pounds by the gauge. What 
is the external work? Ans. 6464 foot-pounds. 

9. What would have been the external work had the air 
expanded adiabatically ? Ans. 4450 foot-pounds. 



74 PERFECT GASES 

10. Find the external work of 2 pounds of air which expand 
adiabatically until the volume is doubled, the initial pressure 
being 100 pounds absolute and the initial temperature 100° F. 
Ans. 36,100 foot-pounds. 

11. Find the external work of one kilogram of hydrogen, 
which, starting with the pressure of 4 atmospheres and with the 
temperature of 500° C, expands adiabatically till the tempera- 
ture becomes 30° C. Ans. 489,000 m.-kg. 

12. Find the exponent for an exponential curve passing 
through the points ^ = 30, v = 1.9, and ^1 = 15, Vi = 9.6. 
Ans. 0.4279. 

13. Find the exponent for a curve to pass through the points 
p = 40, V = 2y and pi = 12, Vi = 6. Ans. 1.0959. 

14. In examples 12 and 13 let ^ be the pressure in pounds on 
the square inch smdv the volume in cubic feet. Find the external 
work of expansion in each case. Ans. 21,900 and 12,010 foot- 
pounds. 

15. Find the intrinsic energy of one pound of nitrogen under 
the standard pressure of one atmosphere and at freezing-point 
of water. Ans. 66,500 foot-pounds. 

16. A cubic foot of air at 492.7° F. exerts 14.7 pounds gauge 
pressure per square inch. How much do its internal energy and 
its entropy exceed those of the same air under standard condi- 
tions? Ans. 5052 foot-pounds; .00912 units of entropy. 

17. Find the increase in entropy of 2 pounds of a perfect gas 
during isothermal expansion at 100° F. from an initial pressure 
of 84.3 pounds gauge and a volume of 20 cubic feet to a final 
volume of 40 cubic feet. Ans. 0.453. 

18. A kilogram of oxygen at the pressure of 6 atmospheres 
and at 100° C. expands isothermally till it doubles its volume. 
Find the change of entropy. Ans. 0.0434. 

19. Twenty pounds of air are heated at a constant pressure 
of 200 pounds absolute per square inch until the volume increases 
from 20 cubic feet to 40 cubic feet. Find the initial and final 
temperatures, the change in internal energy and the increase in 
entropy. How much heat is added? Ans. 80° and 620°; 



EXAMPLES 



75 



increase of intrinsic energy 1,420,000 foot-pounds; increase in 
entropy 3.29; heat 2570 b.t.u. 

20. Suppose a hot-air engine, in which the maximum pressure 
is 100 pounds absolute, and the maximum temperature is 600° F., 
to work on a Carnot cycle. Let the initial volume be 2 cubic 
feet, let the volume after isothermal expansion be 5 cubic feet, 
and the volume after adiabatic expansion be 8 cubic feet. Find 
the horse-power if the engine is double-acting and makes 30 
revolutions per minute. Ans. 8.3 horse-power. 



CHAPTER VI. 

SATURATED VAPOR. 

For engineering purposes steam is generated in a boiler which 
is partially filled with water, and arranged to receive heat from 
the fire in the furnace. The ebullition is usually energetic, and 
more or less water is mingled with the steam; but if there is a 
fair allowance of steam space over the water, and if proper 
arrangements are provided for with drawing the steam, it will 
be found when tested to contain a small amount of water, usu- 
ally between half a per cent and a per cent and a half. Steam 
which contains a considerable percentage of water is passed 
through a separator which removes almost all the water. Such 
steam is considered to be approximately dry. 

If the steam is quite free from water it is said to be dry and 
saturated; steam from a boiler with a large steam space and 
which is making steam very slowly is nearly if not quite dry. 

Steam which is withdrawn from the boiler may be heated to a 
higher temperature than that found in the boiler, and is then said 
to be superheated. 

Our knowledge of the properties of saturated steam and other 
vapors is due mainly to the experiments of Regnault,* who 
determined the relations of the temperature and pressure, the 
total heat of vaporization, and the heat of the Uquid for many 
volatile liquids. Since his time, Rowland's determination of 
the mechanical equivalent of heat, gave a more exact determi- 
nation of the specific heat of water at low temperatures, and 
recently Dr. Barnes has given a very precise determination of 
that property for water. Again, certain work by Knoblauch, 
Linde, and Klebe, has given us a good knowledge of the properties 

* Memoires de VlnstitiU de France, etc., tome xxvi. 
76 



PRESSURE OF SATURATED VAPORS 77 

of superheated steam which can be extended to give the specific 
volume of saturated steam over a considerable range of temper- 
ature. At the time when the first edition of this work was pre- 
pared it appeared desirable to compute tables of the properties 
of saturated vapor, taking advantage of Rowland's work, 
and eliminating some uncertainties due to the way in which 
Regnault used his empirical equations in computating tables. 
As all this involved changes of sufficient magnitude to influence 
engineering computations, it seemed necessary to quote the 
original data at length and to give computations in detail. This 
introduction to the chapter on saturated vapors was found to be 
somewhat confusing to students reading it for the first time, and 
since the main points are now commonly accepted, this work is 
given only in the introduction to the " Tables of the Properties of 
Saturated Steam," the reason for printing it being that it is not 
given elsewhere, as the earlier editions have passed out of print. 

Recent correction of the absolute temperature of the freezing- 
point of water by Callendar and the determination of the specific 
heat of water by Barnes make it necessary to recompute the 
" Tables of the Properties of Saturated Steam " which are 
intended to accompany this book, and opportunity is taken to 
introduce further data in those tables, and in addition a table 
has been prepared which will be found to greatly facilitate calcu- 
lations of adiabatic changes of steam and water. 

Pressure of Saturated Vapors. — Regnault expressed the 
results of his experiments on the temperature and pressure of 
saturated vapors in the form of the following empirical equation, 

\ogp= a + 6a:" + c/r (94) 

where p is the pressure, n is the temperature minus the temper- 
ature to of the lowest Hmit of the range of temperature to which 
the equation appHes, i.e., 

n = t — Iq. 

The constants for the above equation as apphed to saturated 
steam have been recomputed and reduced to the latitude of 45°, 
and are as follow: 



78 SATURATED VAPOR 

B. For steam from o° to ioo° C. expressing the pressure in 
mm. of mercury, 

log ^ = a — Ja" + c/?" 

« = 4-7395022 
log b = 0.6117400 
log c — 8.13204 — 10 
log a = 9.996725828 — 10 
log ^ = 0.0068641 



C. For steam from 100° to 220° C. expressing the pressure in 
mm, of mercury, 

«= 5-4575701 

log h = 0.41 2002 1 
log c = 7.7416789 — 10 
log a = 9. 99741 1 296 — 10 

log ^ = 0.007641 801 ' 

n ^ t ~ 100 

B^. For steam from 32° to 212° F. in pounds per square inch, 

a = 3.025906 
log h = 0.61 1 7400 
log c = 8.13204 — 10 
logo: = 9.998181015 — 10 
log/? = 0.0038134 

w = i — 32 

Cj. For steam from 212° to 428° F. in pounds per square 
inch, 

« = 3-743976 

log h = 0.4120021 
log c = 7.74168 — 10 
log a = 9.998561831 — 10 
log/? = 0.0042454 
n = t — 212 



Pressure of Other Vapors. — Regnault determined also the 
pressure of a large number of saturated vapors at various tem- 
peratures, and deduced equations for each in the form of equa- 
tion (94). The equations and the constants as determined by 
him for the commoner vapors are given in the following table: 



DIFFERENTIAL COEFFICIENT 



79 





log/ 


a 


h 


c 


Alcohol ....... 

Ether . 

Chloroform ...... 

Carbon bisulphide . . 
Carbon tetrachloride 


a + &a~ - c/^^ 
a - fttt" - c^" 
a - ha"" - c^l 

a — ban — c^8 


5.4562028 
5.0286298 
5.2253893 
5. 401 I 662 
12.0962331 


4.9809960 
0.0002284 
2.9531281 
3.4405663 
9.1375180 


0.0485397 
3.1906390 
0.0668673 
0.2857386 
1.9674890 



Alcohol 

Ether 

Chloroform. » . . , 
Carbon bisulphide . 
Carbon tetrachloride 



log, 



1-99708557 

H"°i45775 
1.9974144 
T. 9977628 
T. 9997120 



log/3 



1.9409485 
1.996877 
1.9868176 
T. 991 1997 
1.9949780 



fl 




t + 


20 


^ + 


20 


t - 


20 


t + 


20 


t + 


20 



- 20°, + 150° c. 

- 20°, + 120° c. 
+ 20°, + 164° c. 

- 20°, + 140° c. 

- 20°, + 188° c. 



Zeuner * states that there is a sHght error in Regnault 's cal- 
culation of the constants for aceton, and gives instead 

log p = a ~ ba^ + c/?"; 

« = 5-3085419; 
log &«** = +0.5312766—0.0026148^; 
logc/?''^ —0.9645222 — 0.0215592 i. 

dp 
Differential Coefficient —-. — From the general form of 



equation (94) we have 



M M M 



(95) 



M being the modulus of the common system of logarithms. 
Differentiating, 

^^ = ^Mog.a.«»+i-clog.^./r; 
or, reducing to common logarithms, 



^?=i^'''"8"-«'' + ^^i°s^-^= 



l_dp_ 
p dt 

i_dp 
p dt 



M' 



= Aa"" + 5/?^ 



* Mechanische Warmetheorie. 



So SATURATED VAPOR 

The constants to be used with equation (95) are: 

French Units. 

B. For o^ to 100° C, mm. of mercury, 

log^ = 8.8512729 — 10; 
logB = 6,69305 - 10; 
log a, = 9.996725828 - 10; 

log /?! = 0.0068641. 

C. For 100° to 220° C, mm. of mercury, 

log^ = 8.5495158 - 10; 
log B = 6.34931 - 10; 
log a, = 9. 99741 1296 — 10; 
log P 1= 0.0076418. 

English Units. 

B,. For 32° to 212° F., pounds on the square inch, 
log .4 = 8.5960005 — 10; 
log B = 6,43778 — 10; 
log ttg = 9.998181015 — 10; 
log ^2 = 0.0038134, 

Cj. For 212° to 428° F., pounds on the square inch, 

log^ = 8.2942434 — 10; 
log B = 0,09403 — 10; 
log a^ = 9. 99856183 1 — 10; 
log ^2 = 0.0042454. 



It is to be remarked that -~ may be found approximately 

at 

by dividing a small difference of pressure by the corresponding 

difference of temperature; that is, by calculating --. With a 

table for even degrees of temperature we may calculate the 
value approximately for a given temperature by dividing the 
difference of the pressures corresponding to the next higher and 
the next lower degrees by two. 

The following table of constants for the several vapors named 
were calculated by Zeuner from the preceding equations for 
temperature and pressure of the same vapors: 



MECHANICAL EQUIVALENT OF HEAT 



8l 



DIFFERENTIAL COEFFICIENT 



p dt 





Sign. 


log (^a") 


log {B^"^) 




yla" 


5^" 




Alcohol 

Ether 


+ 
+ 
4- 
+ 
+ 
+ 


+ 

+ 

+ 


— 1. 1720041 — 0.0029143/ 

— 1.3396624 — 0.0031223/ 

— 1.3410130—0.0025856/ 

- 1.4339778-0.0022372/ 

- 1.8611078-0.0002880/ 

- 1.3268535-0.0026148/ 


— 2.9992701 — 0590515 t 

— 4.4616396+0.0145775 / 


Chloroform 

Carbon bisulphide . . . 
Carbon tetrachloride . . 
Aceton ....... 


— 2.0667124—0.0131824/ 

— 2.0511078—0.0088003/ 

— 1.3812195—0.0050220/ 

— 1.9064582— 0.0215592 / 



Standard Temperature. — It is customary to refer all calcu- 
lations for gases to the standard conditions of the pressure of 
the atmosphere (760 mm. of mercury) and to the freezing-point 
of water. Formerly the freezing-point was taken as the standard 
temperature for water and steam as even now it is the initial point 
for tables of the properties of saturated vapors. But the investi- 
gation of the mechanical equivalent of heat by Rowland resulted 
in a determination of the specific heat of water with much greater 
delicacy than is possible by Regnault ^s method of mixtures, and 
showed that freezing-point is not well adapted for the standard 
temperature for water. It has been the habit of physicists 
for many years to take 15° C. as the standard temperature, 
and this corresponds substantially with 62° F., at which the 
English units of measure are standard. Professor Callendar 
recommends 20° C. as the standard temperature which would 
make a variation of about toVo in the value of the mechanical 
equivalent of heat and in the specific heat of water. 

Mechanical Equivalent of Heat. — The most authoritative 
determination of the mechanical equivalent of heat appears to be 
that by Rowland,* from which the work required to raise the 
temperature of one pound of water from 62° to 63° F. is 

778 foot-pounds. 

This is equivalent to 

427 metre kilograms 

in the metric system. Since his experiments were made this 
important physical constant has been investigated by several 

* Proc. Am. Acad., vol. xv (N. S. vii), 1879. 



82 SATURATED VAPOR 

experimenters, and also a recomputation of his results has been 
made after a recomparison of his thermometers. The conclu- 
sion appears to be that his results may be a little small, but the 
differences are not important, and it is not certain that the con- 
clusion is valid. There seems, therefore, no sufficient reason for 
changing the accepted values given above. 

Heat of the Liquid. — The most reliable determination of the 
specific heat of water is that by Dr. Barnes,* v^ho used an electrical 
method devised by Professor Callendar and himself, and who 
extended the method to and below freezing-point by carefully 
coohng water without the formation of ice, to — 5° C. This 
method gives relative results with great refinement, and gives also 
a good confirmation of Rowland 's determination of the mechan- 
ical equivalent of heat. Dr. Barnes reports values of the specific 
heat of water up to 95° C. In the following table his results are 
quoted from 0° to 55° C.; from 55° to 95° his results have been 
slightly increased to join with results determined by recomput- 
ing Regnault's experiments on the heat of the liquid for water 
(which experiments range from 110° C. to 180° C.) by allowing 
for the true specific heat at low temperature from Dr. Barnes's 
experiments. The maximum effect of modifying Dr. Barnes's 
results is to increase the heat of the liquid at 95° by one- tenth of 
one per cent» 

SPECIFIC HEAT OF [WATER. 



Temperature. 




Temperature. 




Temperature. 








Specific 
Heat. 






Specific 
Heat. 






Specific 
Heat. 














C. 


F. 




C. 


F. 




C. 


F. 







32 


I . 0094 


45 


113 


0.99760 


90 


194 


I . 00705 


5 


41 


1.00530 


50 


122 


. 99800 


95 


203 


1.00855 


10 


50 


1.00230 


55 


131 


0.99850 


100 


212 


I.OIOIO 


15 


59 


I . 00030 


60 


140 


0.99940 


120 


248 


I. 01620 


20 


68 


0.99895 


^5 


149 


I . 00040 


140 


284 


1.02230 


25 


77 


0.99806 


70 


i5« 


I. 001 50 


160 


320 


1.02850 


30 


86 


0-99759 


l^ 


167 


1.00275 


180 


35b 


1.03475 


35 


95 


o- 99735 


80 


176 


I. 00415 


200 


392 


I. 04100 


40 


104 


o- 99735 


«5 


185 


I « 0055 7 


220 


428 


1.04760 



* Physical Review, vol. xv, p. 71, 1902. 



HEAT OF THE LIQUID 83 

Heat of the Liquid. — The heat required to raise one unit of 

weight of any Hquid from freezing-point to a given temperature 

is called the heat of the liquid at that temperature; and also at the 

corresponding pressure. Since the specific heat for water varies 

we may obtain the heat of the liquid by integration as indicated 

by the equation n 

q = \ cdt (96) 

In order to use this equation it would be necessary to obtain 
an empirical equation connecting the specific heat with the 
temperature; such an equation has not been proposed and would 
probably be complex. -Another method is to draw a curve with 
temperatures as abscissae and specific heats as ordinates and inte- 
grate graphically. The fact that the specific heat is nearly 
equal to unity at all temperatures and that consequently the heat 
of the liquid for the Centigrade thermometer is not very different 
from the temperature suggests the following method : 

Let c = 1 -{- k 

when k is the difference between the specific heat and unity at 
any temperature, k being positive or negative as the case may be. 

^^^^ q = t +Jkdt (97) 

which may be obtained by plotting values of k as ordinates and 
integrating graphically, which will have the advantage that the 
required curve may be drawn to a large scale and give correspond- 
ingly accurate results. The values for the heat of the liquid for 
water in the " Tables of the Properties of Saturated Steam " were 
obtained in this way. 

The following table gives equations for the heats of the liquids 
of other substances than water, determined by Regnault. 

HEAT OF THE LIQUID. 

Alcohol ,.,... o , q= 0.54754^-1- 0.0011218/2 

-|- 0.000002206/^ 
Ether .. = ,,....,...., ^ = 0.52901 /-(- 0.0002959/^ 

Chloroform q= 0.23235/-}- 0.0000507/^ 

Carbon bisulphide .,.,.„..,$= 0.23523 /-f 0.0000815/^ 

Carbon tetrachloride ^ = o. 19798 / 4- 0.0000906 /^ 

Aceton c q = 0.50643/4- 0.0003965/^ 



84 SATURATED VAPOR 

The specific heat for any of these Hquids may be obtained by 
differentiation; for example, the specific heat for alcohol is 

c = 0.54754 + 0.0022436 / + 0.000006618 f^ 

Total Heat. — This term is defined as the heat required to 
raise a unit of weight of water from freezing-point to a given 
temperature, and to entirely evaporate it at that temperature. 
The experiments made by Regnault were in the reverse order; 
that is, steam was led from a boiler into the calorimeter and 
there condensed. Knowing the initial and final weights of 
the calorimeter, the temperature of the steam, and the initial 
and final temperatures of the water in the calorimeter, he was 
able, after applying the necessary corrections, to calculate the 
total heats for the several experiments. 

The results from these experiments are represented by the 
following equations: 

For the metric system, 

H = 606.5 + 0.305 t (98) 

For the English system, 

H = 1091.7 + 0.305 (/ — 32) : . . (99) 

An investigation of the original experimental results, 
allowing for the true specific heat of the water in the calorimeter, 
showed that the probable errors of the method of determining 
the total heat were larger than the deviations of the true specific 
heats from unity, the value assumed by Regnault; and, further, 
it appeared that his equation represents our best knowledge of 
the total heat of steam. There appears to be no reason for 
changing this equation till new experimental values shall be 
supplied. The deviation of individual experimental results 
from corresponding computations by the equation is Kkely to be 
one in five hundred. There is further some uncertainty whether 
the method of drawing steam from the boiler did not involve 
some error due to entrained moisture. The best check upon 
Regnault 's results is a comparison with Knoblauch's work on 
superheated steam. 



SPECIFIC VOLUME OF LIQUIDS 85 

Regnault gives the equations following for other liquids; 

Ether H = 94 +0.45/ - 0.00055556 f^ 

Chloroform il = 67 + 0.1375^ 

Carbon bisulphide H= 90 + o. 14601 «— 0.0004123 /^ 

Carbon tetrachloride H = 52 + 0.14625 f — 0.000172 ^^ 

Aceton il = 140.5 + 0.36644 ^ — 0.000516 /^ 

Heat of Vaporization. — If the heat of the liquid be sub- 
tracted from the total heat, the remainder is called the heat of 
vaporization, and is represented by r, so that 

r = H — q . (100) 

Specific Volume of Liquids. — The coefficient of expansion of 
most liquids is large as compared with that of solids, but it is 
small as compared with that of gases or vapors. Again, the 
specific volume of a vapor is large compared with that of the 
liquid from which it is formed. Consequently the error of neg- 
lecting the increase of volume of a liquid with the rise of temper- 
ature is small in equations relating to the thermodynamics of a 
saturated vapor, or of a mixture of a liquid and its vapor when 
a considerable part by weight of the mixture is vapor. It is 
therefore customary to consider the specific volume of a liquid 
cr to be constant. 

The following table gives the specific gravities and specific 
volumes of liquids: 

SPECIFIC GRAVITIES AND SPECIFIC VOLUMES OF LIQUIDS. 



Alcohol 

Ether . 

Chloroform ... 
Carbon bisulphide . 
Carbon tetrachloride 

Aceton 

Sulphur dioxide . 

Ammonia 

Water 



Specific 
Gravity 
compared 
with Water 
at 4° C. 



0.80625 
0.736 

1-527 
I . 2922 
1.6320 
0.81 

T.4336 
0.6364 
I 



Specific Volume. 



Cubic Metres. Cubic Feet 



o 001240 
o 001350 
0.000655 
o 000774 
0.00613 
0.00123 
0.0006981 
O.OOI57I 

O.OOI 



O.OII2 
0.0252 
0.01602 



86 



SATURATED VAPOR 



Experiments were made by Hirn* to determine the volumes 
of liquid at high temperatures compared with the volume at 
freezing-point, by a method which was essentially to use them 
for the expansive substance of a thermometer. The results are 
given in the following equations: 

SPECIFIC VOLUMES OF HOT LIQUIDS. 



Water, 

ioo° C. to 200° C. 

(Vol. at 4° = unity.) 



Alcohol, 

30° C. to 160° C. 

(Vol. at 0° = unity.) 



Ether, 

30° C. to 130° C. 

(Vol. at 0° = unity.) 



Carbon Bisulphide, 

30° C. to 160° C. 

(Vol. at 0° = unity.) 



Carbon Tetrachloride, 

30° C. to 160° C. 
(Vol. at 0° = unity.) 



V = I -{- 0.00010867875 t 

+ 0.0000030073653 f^ 
+ 0.000000028730422 t^ 

— 0.0000000000066457031 t' 

V — 1 -\- 0.00073892265 t 

+ 0.00001055235 1^ 

— 0.000000092480842 t^ 

+ 0.00000000040413567 f* 

V = I + 0,0013489059 t 

+ 0.0000065537/^ 

— 0.000000034490756 <^ 
+ 0.00000000033772062 t* 

•y = I + 0.0011680559/ 

+ 0.0000016489598/' 

— 0.0000000008 1 1 19062 t^ 
+ 0.000000000060946589/* 

V = I + 0.0010671883 / 

+ 0.0000035651378/' 

— 0.00000001494928 1 /^ 

+ o . 000000000085 182318/* 



Logarithms. 



6.0361445 - 10 
4.4781862 — 10 

1. 4583419 - 10 
8.8225409 — 20 

6.8685991 — 10 
3.0233492 - 10 
2.9660517 — 10 
0.6065278 — 10 

7.1299817 — 10 
4.8164866 — 10 
2.5377028 - 10 
0-5285571 - 10 

7.0674636 — 10 
4.2172103 — 10 
0.9091229 — 10 
9.7849494 - 20 

7.0282409 — 10 
4-5520763 - 10 
2. 174620^ — 10 
9-9303494 - 20 



Quality or Dryness Factor. — All the properties of saturated 
steam, such as pressure, volume and heat of vaporization, depend 
on the temperature only, and are determinable either by direct 
experiment or by computation, and are commonly taken from 
tables calculated for the purpose. 

Many of the problems met in engineering deal with mixtures of 
liquid and vapor, such as water and steam. In such problems 
it is convenient to represent the proportions of water and steam 
by a variable known as the quality or the dryness factor; this 

* Annales de Chimie et de Physique, 1867. 



GENERAL EQUATION 87 

factor, Xj is defined as that portion of a pound of the mixture 
which is steam; the remnant, 1 — x, is consequently water. 

Specific Volume of Wet Steam. — Let the specific volume of 
the saturated vapor be 5 and that of the liquid be <r; then the 
change of volume is s — a- = u on passing from the liquid to 
the vaporous state. If a pound of a homogeneous mixture of 
water and steam is x part steam, then the specific volume may 
be represented by 

V = xs -\- {1 ~ x) a- = xu + or . . ... (lOl) 

where u is the increase of volume due to vaporization. 

Internal and External Latent Heat. — The heat of vaporiza- 
tion overcomes external pressure, and changes the state from 
liquid to vapor at constant temperature and pressure. The 
external work is 

p {s ~ a) = pu, 

and the corresponding amount of heat, or the external latent 
heat, is 

Ap (s — a-) = Apu. 

The heat required to do the disgregation work, or the internal 
latent heat, is 

p = r — Apu ....'... (102) 

General Equation. — In order to apply the general thermo- 
dynamic method to a mixture of a liquid and its vapor, it is 
customary to write a differential equation involving the tem- 
perature t, the quality x, . the specific heats of water and steam c 
and h, and the heat of vaporization r; these three last properties 
are assumed to be functions of the temperature only. 

The principal result of the application of the general method 
to such an equation is a formula for calculating the specific 
volume J, as will appear later. Following the general method, a 
special derivation of the formula for s will be given which may 
be preferred by some readers. 

When a mixture of liquid and its vapor receives heat there is 



88 SATURATED VAPOR 

in general an increase in the temperature of the portion x of 
vapor and in the portion i — x oi Kquid, and there is a vaporiza- 
tion of part of the liquid. Taking c for the specific heat of the 
liquid and h for the specific heat of the vapor, while r is the heat 
of vaporization, we shall have for an infinitesimal change, 

dQ = hxdt + c (i — x) dt -\- rdx .(103) 

Application of the First Law. — The first law of thermo- 
dynamics is applied to equation (103) by combining it with 
equation (16), so that 

dQ = A (dE -I- pdv) = hxdt -\- c (i — x) dt + rdx; 

I T 

dE = — [hx 4- c (i — x)] dt -\- -: dx — pdv. 

Jx Jx 

Now 1' is a function of both t and x, as is evident from equation 
(loi), in which w is a function of /; consequently, 

dv = -TT dt -\- -^r- dx. 
bt ox 



But E being expressed in terms of t and x gives 

B^ E _ S^£ 
Bt 8x Bx Bt 



so 



B ii,, , ,-, Bv i B fr Bv\ 

that _J-[/.. + .(._.)]-^-J=_(--^-). 



Bearing in mind that all the functions but x and v are functions 
of / only, the differentiation gives 

i_ , V 3^ u 1 dr dp_^ 3^ i; 

A^ ^""^"^ BtBx~ A dt dt Bx ^ Bx Bt ' 



FIRST AND SECOND LAWS COMBINED 89 

Equation (loi) gives 







dv 
dx 


w, 


and 




hH 


B'v 


V 




BtBx 


SxSt' 


so that the above 


equation 


reduces to 



| + .-.^.,f .... .(.04) 



Application of the Second Law. — The second law of thermo- 
dynamics makes 

T ^ 

for a reversible process, so that the general equation (103) may 
be reduced to 

T T T 

Bx Bt Bt Bx 

B hx — c (1 — x) B r 
''' B^ T ^ Bt f' 

h — c at 



But 



dr , J r / \ 

dt T . ^ ^^ 



First and Second Laws Combined. — The combination of 
equations (104) and (105) gives 

r = AuT ^ (106) 



p 






a 


T 


• \ 


\ 




\ 


d 


T-AT 


c 







V 



go SATURATED VAPOR 

Special Method. — The preceding equation may be obtained^ 
by a special method making use of the 
diagram abed in Fig. 30 which repre- 
sents Camot 's cycle for a mixture of a 
liquid and its vapor, the change of 
temperature A T being very small. Let 
a represent the volume of one pound of 
water at the temperature T, and b the 
Fig. 30. volume of one pound of steam at the same 

temperature and pressure. The line ab 
therefore represents the vaporization of one pound of water at 
constant temperature, involving the application of the heat of 
vaporization r, and the increase of volume 



where s and cr are the specific volumes of steam and water. By 

the second law of thermodynamics the efficiency of this cycle will 

be 

T — (T — AT) _ AT 

T ~ T ' 

so that the heat changed into work will be 

rAT 



But by the first law of thermodynamics this heat is equivalent 
to the external work, which in this case is approximately equal 
to the increase of volume u multiplied by the change of pressure 
Ap; consequently, 

^^^ A^ 

J^ = uAp, 

or, at the limit as AT approaches zero, 

dt 



SPECIFIC VOLUME AND DENSITY 91 

Specific Volume and Density. — The most important result of 
the application of the methods of thermodynamics to the prop- 
erties of saturated vapor is expressed by equation (106), which 
gives a method of calculating the specific volume; thus, 

^ = ^ + -=^^ + - (107) 

dt 

The numerical value of o" for water for French units is 0.00 1, 
and for English units is -^ = 0.016, nearly. The density, or 
weight of a unit of volume, is of course the reciprocal of the 
specific volume. 

It is of interest to consider the degree of accuracy that may be 
expected from this method of calculating the density of saturated 
vapor. The value of r depends on H and q, the total heat and the 
heat of the liquid ; the latter is now well known, but the total heat 
is probably in doubt to the extent of ^^^o and may be more. The 
absolute temperature T appears to be better known and may be 
subject to an error of no more than toVo or Woo ; and the mechan- 
ical equivalent of heat — is perhaps as well determined as the 

absolute temperature. The least satisfactory factor in the 

dj) 
expression is the differential coefficient -j- , which is derived by 

differentiating one of the empirical equations on pages 78 and 79. 
It is true that the resulting equations on pages 79 and 80 afford a 
ready means of computing values of the coefficient with great 
apparent accuracy, but some idea of the essential vagueness of 
the method may be obtained by comparing computations of the 
specific volume of saturated steam at 212° C, a point for which 
either equation B^ or equation C^ will give the pressure as 14.6967 
pounds per square inch. The specific volume by aid of equation 
(107 ), using equation B^ for determining the differential coefficient, 
is 26.62, while the differential coefficient from equation C^ gives 
26.71; the discrepancy is about ^^^; or if the mean 26.66 betaken 
as the probable value, either computed value is subject to an 
error of ^^0. 



92 



SATURATED VAPOR 



Experimental Determinations of Specific Volume. — By far the 

best direct determinations of the specific volumes of saturated 
steam are those reported by Knoblauch, Linde, and Klebe, as 
expressed by their characteristic equation for superheated steam 
given on page no. These experiments determined the pres- 
sures for various temperatures at constant volume, and the 
results were so treated as to give the volume at saturation by 
exterpolation with great certainty. The following is a com- 
parison of specific volume determined by them and volumes com- 
puted by equation (107). 

SPECIFIC VOLUMES OF SATURATED STEAM. 
By Knoblauch, Linde, and Klebe. 





Volume Cu. M. 




Volume Cu. M. 




Volume Cu. M. 


Temper- 




Temper- 




Temper- 
















ature. 


Experi- 


Com- 


ature. 


Experi- 


Com- 


ature. 


Experi- 


Com- 




mental. 


puted. 




mental. 


puted. 




mental. 


puted. 


100 


1.674 


1.665 


130 


0.6690 


. 6604 


160 


0.3073 


0.3039 


105 


1.420 


I. 412 


135 


0.5822 


0-5747 


165 


0.2729 


0.2703 


IIO 


I. 211 


I. 212 


140 


0.5091 


0.5021 


170 


0.2430 


O.2411 


"5 


1-037 


1.027 


145 


0.4466 


0.4405 


H^ 


0.2170 


0.2157 


120 


0.8922 


0.8826 


150 


0.3921 


0.3880 


180 


0.1943 


0.1934 


125 


0.7707 


0.7617 


155 


0.3470 


0.3428 









Nature of the Specific Heats. — In the appHcation of the gen- 
eral thermodynamic method on page SS the term h is intro- 
duced to represent the specific heat of saturated steam, and there 
is sonie interest in the determination of the true nature of this 
property, which clearly cannot be a specific heat at constant 
pressure, nor a specific heat at constant volume, since both pressure 
and volume change with the temperature. The specific heat of 
the liquid c properly is affected by the same consideration, but 
as the increase of volume is small and is neglected in thermo- 
dynamic discussions, the importance of the consideration is much 
less. The specific heat h of saturated vapor is the amount of 
heat necessary to raise the temperature of one pound of the 
vapor one degree, under the condition that the pressure shall 



NATURES OF SPECIFIC HEATS 93 

increase with the temperature, according to the law for saturated 
vapor. 

Equation (105) gives a ready way of calculating the specific 
heat for a vapor, for from it 

, dr r 

Now r may be readily expressed as a function of /, and then 

d/Y 
by differentiation — may be determined. For steam 

Culr 

r = H - q= 606.5 + 0-305 i-[qx + c {t- /J], 

in which t^ is the temperature at the beginning of the range, as 
given by the table on page 80, within which / may fall. There- 
fore 

dr 

dt 



and 



h = 0.305 — — 



For other vapors the equations, deduced from the empirical 
equations for q and H on pages d>2i and 85, are somewhat more 
complicated, but they involve no especial difficulty. 

The following table gives the values of h for steam at several 
absolute pressures: 

SPECIFIC HEAT OF STEAM. 

Pressures, lbs. per sq. in., p S 50 100 200 300 

Temperatures, ^° F. . . . 162.3 280.9 327.6 381.7 4i7-4 

Specific heat, /t —1.30 ~o-93 —0.82 —0.70 —0.63 

The negative si^n shows that heat must be abstracted from 
saturated steam when the temperature and pressure are increased, 
otherwise it will become superheated. On the other hand, 
steam, when it suddenly expands with a loss of temperature and 
pressure, suffers condensation, and the heat thus liberated sup- 
plies that required by the uncondensed portion. 



94 SATURATED VAPOR 

Hirn * verified this conclusion by suddenly expanding steam in 
a cylinder with glass sides, whereupon the clear saturated steam 
suffered partial condensation, as indicated by the formation of a 
cloud of mist. The reverse of this experiment showed that steam 
does not condense with sudden compression, as shown by Cazin. 

Ether has a positive value for h. As the theory indicates, a 
cloud is formed during sudden compression, but not during sud- 
den expansion. 

The table of values of h for steam shows a notable decrease 
for higher temperatures, which indicates a point of inversion at 
which h is zero and above which h is positive, but the tempera- 
ture of that point cannot be determined from our experimental 
knowledge. For chloroform the point of inversion was calcu- 
lated by Cazin f to be 123^.48, and determined experimentally by 
him to be between 125° and 129°. The discrepancy is mostly 
due to the imperfection of the apparatus used, which substituted 
finite changes of considerable magnitude for the indefinitely 
small changes required by the theory. 

Isothermal Lines. — Since the pressure of saturated vapor is a 
function of the temperature only, the isothermal line of a mixture 
of a liquid and its vapor is a line of constant pressure, parallel to 
the axis of volumes. Steam expanding from the boiler into the 
cylinder of an engine follows such a line; that is, the steam- line 
of an automatic cut-off engine with ample ports is nearly parallel 
to the atmospheric line. 

The heat required for an increase of volume at constant press- 
ure is 

Q = r {x^ — x^) (108) 

in which r is the heat required to vaporize one pound of liquid, 
and x^ and x^ are the initial and final qualities, so that x.^ — x^ 
is the weight of Uquid vaporized. 

The external work done during an isothermal expansion is 

W = p (v^ — vj = pu (x^ — x^) . . . , (109) 

* Bulletin de la Societe Ind. de Mulhouse, cxxxiii. 
t Comptes rendus de VAcademie des Sciences, Ixii. 



ISOENERGIC OR ISODYNAMIC LINES 



95 



Intrinsic Energy. — Of the heat required to raise a pound of 
any Hquid from freezing-point to a given temperature and to 
completely vaporize it at that temperature, a part q is required 
to increase the temperature, another part p is required to change 
the state or do disgregation work, and a third part Apu is required 
to do the external work of vaporization. Consequently for com- 
plete vaporization we may have, 

Q = A{S + I-^W) = q + p + Apu = H, 

For partial vaporization the heat required to do the disgrega- 
tion work will be x/3, and the heat required to do the external 
work will be Apxu. Therefore the heat required to raise a pound 
of a liquid from freezing-point to a given temperature and to 
vaporize x part of it will be 

Q = q + xp + Apxu = A{E + W) 

where E is the increase of intrinsic energy from freezing-point. 
It is customary to consider that 

E = ~^{xp + q) (no) 

represents the intrinsic energy of one unit of weight of a mixture 
of a liquid and its vapor. 

Isoenergic or Isodynamic Lines. — If a change of a mixture 
of a liquid and its vapor takes place at constant intrinsic energy, 
the value of E will be the same at the initial and final conditions, 
and 

?2 — ?i + ^292 — ^iPi = o .... (in) 

which equation, with the formulae 

v^ = x^u^ + o"; 1^1 = x^u^ + o" . . . . (112) 

enable us to compute the initial and final volumes. If desired, 
intermediate volume corresponding to intermediate temperature 
can be computed in the same way, and a curve can be drawn 
in the usual way with pressures and volumes for the coordinates. 
Eor example, if a mixture of -^0 steam and tV water expands 



96 SATURATED VAPOR 

isoenergically from loo pounds absolute to 15 pounds absolute, 
the final condition will be 

_ ^1 - ^2 + ^iPi _ 297.9 - 181.8 + o.Q X 802.8 _ 
""'- p, ~ 892.6 -0-9395- 

The initial and final specific volumes are 
v^ = x^u^ + «r = 0.9 (4.403 — 0.016) + 0.016 = 3.964; 
v^ = x^u^ -\- a = 0.9395 (26.15 "~ o-oi6) + 0.016 = 24.54. 

The converse problem requiring the pressure corresponding to 
a given volume cannot be solved directly. The only method 
of solving such a problem is to assume a probable final pressure 
and find the corresponding volume; then, if necessary, assume 
a new final pressure larger or smaller as may be required, and 
solve for the volume again; and so on until the desired degree 
of accuracy is obtained. 

This method does not give an explicit equation connecting the 
pressures and volumes, but it will be found on trial that a curve, 
drawn by the process given above can be represented fairly well 
by an exponential equation, for which the exponent can be 
determined by the method on page 66. 

Having given or determined the initial and final volumes, the 
exponential equation may be determined, and then the external 
work may be calculated by the equation 

For example^ the exponent for the equation representing the 
expansion of the above problem is 

^ _ log p, - log p , _ log 100 - log 15 _ ^^^^^^ 
log v^ — log v^ log 24.54 — log 3.964 

and the external work of expansion is 

„r 100 X 144 X ^.064 ( I'x.q6a\°-°'^^) -^ ,, 

W = ^^ o_v_if 1 J _ ( v^ V ^ J f ^ 100,000 ft.-lbs. 

1.041 — I ( \24.54/ ) 



ENTROPY OF THE LIQUID gy 

Since there is no change in the intrinsic energy during an 
isoenergic expansion, the external work is equivalent to the heat 
applied. Thus in the example just solved the heat applied is 
equal to 

100,000 ^ 778 = 129B.T.U. 

There is little occasion for the use of the method just given, 
v^hich is fortunate, as it is not convenient. 

Entropy of the Liquid. — Suppose that a unit of weight of a 
liquid is intimately mingled with its vapor, so that its tempera- 
ture is always the same as that of the vapor; then if the pressure 
of the vapor is increased the liquid will be heated, and if the 
vapor expands the liquid will be cooled. So far as the unit of 
weight of the liquid under consideration is concerned, the pro- 
cesses are reversible, for it will always be at the temperature of 
the substance from which it receives or to which it imparts heat, 
i.e., it is always at the temperature of its vapor. 

The change of entropy of the liquid can therefore be calculated 
by equation (37), 

which may here be written 

^=/f=/f (-3) 

On page 83 it is suggested that the specific heat of water for 
temperature Centigrade may be expressed as follows: 

c =^ 1 + k 

where ^ is a small corrective term that may be positive or negative 
as the case may be. Using this correction, equation (113) may 
be written 

. rdt , rkdt . ^ 



gS SATURATED VAPOR 

The first term can readily be integrated and computed, and the 
second term, which is small, can be determined graphically, so 
that the expression for entropy, of water becomes 

= \og.^+ fk^. . . . . .(115) 

The columns of entropy of water in the tables were determined 
in this manner. 

In ithe discussion of entropy on page 31 it was pointed out 
that there is no natural zero of entropy corresponding to the abso- 
lute zero of temperature. It is customary to treat the freezing- 
point of water as the zero of entropy both for that liquid and 
for other volatile liquids; some liquids therefore have negative 
entropies at temperatures below freezingr point of water in the 
appropriate tables of their properties. 

For a liquid like ether which has the heat of the liquid repre- 
sented by an empirical equation, 

q = 0.52901 / + 0.0002959 t^, 

the specific heat is first obtained by differentiation, giving 

c = 0.52901 + 0.0005918 /. 

Then the increase of entropy above that for the freezing-point of 
water may be obtained by aid of equation (113), which gives for 
ether with the French system of units, 

^^Jm )°-5290i + 0.0005918 (T- 273) |y; 

•*• ^^J273 (0-3670 Y + 0-0005918 c^^j; 

I. 

T 

/. 0= 0.0005918 (T — 273) -f 0.3670 loge 



273 



T 

^= 0.0005918 / + 0.3670 loge^ (116) 

273 



ENTROPY OF A MIXTURE OF A LIQUID 99 

For temperatures below the freezing-point of water, equation 
(116) gives negative numerical results. 

Other liquids for which equations for the heat of the liquid 
are given on page 83, may be treated in a similar method. 

Entropy due to Vaporization. — When a unit of weight of a 
liquid is vaporized r thermal units, equal to the heat of vaporiza- 
tion, must be applied at constant temperature. Treating such 
a vaporization as a reversible process, the change of entropy may 
be calculated by the equation 

> — <^o ^ ^ 

This property is given in the " Tables for Saturated Steam," 
but not in general for other liquids. 

Entropy of a Mixture of a Liquid and its Vapor. — The increase 
in entropy due to heating a unit of weight of a liquid from freez- 
ing-point to the temperature t and then vaporizing x portion of 
it is 

where 6 is the entropy of the liquid, r is the heat of vaporization, 

r 

and T is the absolute temperature. For steam — may be taken 

from the tables; for other vapors it must usually be calculated. 

For any other state determined by x^ and t^ we shall have, for 
the increase of entropy above that of liquid at freezing-point. 

The change of entropy in passing from one state to another 
is ^ 

<\>-<\>. = ^ + e-^-e, . . . („7) 

Whlen the condition of the mixture of a liquid and its vapor 
is given by the pressure and value of x, then a table giving the 
properties at each pound may be conveniently used for this work. 



lOO SATURATED VAPOR 

Adiabatic Equation for a Liquid and its Vapor. — During an 

adiabatic change the entropy is constant, so that equation (117) 
gives 



I + 0^^ :^+e, ..... (118) 

When the initial state, determined by x^ and t^ or p^^ is known 
and the final temperature t^, or the final pressure p2, the final 
value x^ may be found by equation (118). The initial and final 
volumes may be calculated by the equations 

v^ = x^u^ + a- and v^ = x^u.^ + o" . . . (119) 

Tables of the properties of saturated vapor commonly give the 

specific volume s^ but 

5 = W + cr. 

The value of cr for water is 0.016, and for other liquids will be 
found on page 85. 

For example, one pound of dry steam at 100 pounds absolute 
pressure will have the values 

h = 327°-6 F., ri = 884.0, e^ = 0.4733, ^1 = I- 
If the final pressure is 15 pounds absolute, we have 
/2 = 213°. o F., r^ = 965.1, ^2 = 0.3143; 

whence 

884.0 , Q6t;.i:x;2 , 

788.3 ^^^^ 673.7 ^ ^^' 

.*. x^ = 0.894. 

The initial and final volumes are 

^1 = s^ = 4.40 

V2 = ^2^2 + ^ = 23.4. 

Problems in which the initial condition and the final tem- 
perature or pressure are given may be solved directly by aid of 
the preceding equations. Those giving the final volume instead 



ADIABATIC EQUATION FOR A LIQUID lOI 

of the temperature or pressure can be solved only by approxi- 
mations. An equation to an adiabatic curve in terms of p and v 
cannot be given, but such a curve for any particular case may 
be constructed point by point. 

Clausius and Rankine independently and at about the same 
time deduced equations identical with equations (117) and 
(118), but by methods each of which differed from that given 
here. 

Rankine called the function 

T 

the thermodynamic function ; Clausius called it entropy. 

In the discussion of the specific heat h oi a saturated vapor, it 
appeared that the expansion of dry saturated steam in a non- 
conducting cyhnder would be accompanied by partial conden- 
sation. The same fact may be brought out more clearly by the 
above problem. 

On the other hand, h is positive for ether, and partial conden- 
sation takes place during compression in a non-conducting 
cylinder. 

For example^ let the initial condition for ether be 

ti = 10° C ., r^ = 93.12, B = 0.0191, JCj = I, 

and let the final conditions be 

/j = 120° C, ^2 = 72.26, ^2 = 0-2045; 

, QS-I2 , 72.26X2 , 

then -^ h 0.0191 = + 0.2045, 

283 393 

and X2 = 0.724. 

Equation (118) apphes to all possible mixtures of a liquid and 
its vapor, including the case oi x^ = o or the case of liquid with- 
out vapor, but at the pressure corresponding to the temperature 
according to the law of saturated vapor. When applied to hot 
water, this equation shows that an expansion in a non-conduct- 
ing cylinder is accompanied by a partial vaporization. 



I02 SATURATED VAPOR 

There is some initial state of the mixture such that the value 
of X shall be the same at the beginning and at the end, though it 
may vary at intermediate states. To find that value make X2 = 
x^ in equation (118) and solve for x^, which gives 

X = AizA_. 



'2 _ '1 

The value of x^ for steam to fulfil the conditions given varies 
with the initial and final temperatures chosen, but in any case it 
will not be much different from one half. It may therefore be 
generally stated that a mixture of steam and water, when 
expanded in a non-conducting cylinder, will show partial con 
densation if more than half is steam, and partial evaporation if 
more than half water. If the mixture is nearly half water and 
half steam, the change must be investigated to determine whether 
evaporation or condensation will occur; but in any case the 
action will be small. 

External Work during Adiabatic Expansion. — Since no heat 
is transmitted during an adiabatic expansion, all of the intrinsic 
energy lost is changed into external work, so that, by equation 
(no), 

1^ = ^1 - ^2 = J (?1 - ?2 + ^£x — ^2P2) ' ' (120) 

For example, the external work of one pound of dry steam in 
expanding adiabatically from 100 pounds to 15 pounds absolute 
is 

W = 778 (297.9 — 181.8 + I X 802.8 — 0.894 X 892.6) 

IF = 120.2 X 778 = 93,500 foot-pounds. 

Attention should be called to the unavoidable defect of this 
method of calculation of external work during adiabatic expan- 
sion, in that it depends on taking the difference of quantities 
which are of the same order of magnitude. For example, the 
above calculation appears to give four places of significant figures, 



EXTERNAL WORK DURING ADIABATIC EXPANSION 



103 



while, as a matter of fact, the total heat H from which p is derived 

is affected by a probable error of or perhaps more. Both 

the quantities 

q^ + x^p^ and q^ + x^p^ 

have a numerical value somewhere near 1000, and an error of 

is nearly equivalent to two thermal units, so that the probable 

error of the above calculation is nearly two per cent. For a 
wider range of temperature the error is less, and for a narrower 
range it is of course larger. This matter should be borne in 
mind in considering the use of approximate methods of calcula- 
tions; for example, the temperature- entropy diagram to be dis- 
cussed later. 

The adiabatic curve cannot be well represented by an expo- 
nential equation; for if an exponent be determined for such a 
curve passing through points representing the initial and final 
states, it will be found that the exponent will vary widely with 
different ranges of pressure, and still more with different initial 
values of x\ and that, further, the intermediate points will not be 
well represented by such an exponential curve even though it 
passes through the initial and final points. 

This fact was first pointed out by Zeuner, who found that the 
most important element in determining n was x^, the initial con- 
dition of the mixture. He gives the following empirical formula 
for determining w, which gives a fair approximation for ordinary 
ranges of temperature : 

n = 1.035 + cioorVj. 

There does not appear to be any good reason for using an 
exponential equation in this connection, for all problems can be 
solved by the method given, and the action of a lagged steam- 
engine cylinder is far from being adiabatic. An adiabatic line 
drawn on an indicator-diagram is instructive, since it shows 
to the eye the difference between the expansion in an actual 
engine and that of an ideal non-conducting cylinder; but it can 



I04 



SATURATED VAPOR 



be intelligently drawn only after an elaborate engine test. For 
general purposes the hyperbola is the best curve for comparison 
with the expansion curve of an indicator-diagram, for the reason 
that it is the conventional curve, and is near enough to the curve 
of the diagrams from good engines to allow a practical engineer 
to guess at the probable behavior of an engine, from the diagram 
alone. It cannot in any sense be considered as the theoretical 
curve. 

Temperature-Entropy Diagram. — If the entropies of the 
liquid and the entropies of vaporization for steam are plotted with 
temperature for ordinates we get a diagram like 30a; very com- 
monly absolute temperatures 
are taken in drawing the dia- 
gram in order to emphasize 
the role played by absolute 
temperatures in the deter- 
mination of the efficiency of 
Carnot 's cycle. It would seem 
better to take the temperature 
by the centigrade or the Fah- 
renheit thermometer, as they 
are the basis of steam-tables, 
and the temperature- entropy diagram is the equivalent of such a 
table. 

Now the entropy of a mixture containing x part steam is 




Fig. 30a. 



-}- X 



r 



so that the entropy of a mixture containing x part of steam can 
be determined by dividing the line such as de (which represents 
the entropy of vaporization) in the proper ratio. 



dc 
de 



= X. 



It is convenient to divide the several lines like ah and de into 
tenths and hundredths, and then, if an adiabatic expansion is 



TEMPERATURE-ENTROPY DIAGRAM 105 

represented by a vertical line like be, the entropy at c may be 
determined by inspection of the diagram. Conversely, by noting 
the temperature at which a given line of constant entropy crosses 
a line of given quality we may determine the temperature to 
which it is necessary to expand to attain that quality, a determina- 
tion which cannot be made directly by the equation. 

When a temperature- entropy diagram is used as a substitute 
for a "Table of the Properties of Saturated Steam," it is custom- 
ary to draw the lines of constant quality or dryness factor, and 
other lines like constant volume lines and lines of constant heat 
contents or values of the expression 

xr + q, 

the use of which will appear in the discussion of steam-engines 
and steam-turbines. 

To get a series of constant volume lines we may compute the 
volume for each quality x^ = .i^, x^ = .2, x = .3, etc., by the 
equation 

V = XU + (T, 

and since the volume increases proportionally to the increase in 
X, we may readily determine the points on that line for which 
the volume shall be whole units, such as 2 cubic feet, 3 cubic feet, 
etc. Points for which the volumes are equal may now be con- 
nected by fair curves, so that for any temperature and entropy the 
volume may readily be estimated. 

Curves of equal heat contents can be constructed in a similar 
way. 

If desired, a curve of temperatures and pressures can be drawn 
so that many problems can be solved approximately by aid of the 
compound diagram. 

At the back of this book a temperature- entropy diagram will 
be found which gives the properties of saturated and superheated 
steam. It is provided with a scale of temperatures at either 
side, and a scale of entropies at the bottom, while there is a scale 
of pressure at the top. 



Io6 SATURATED VAPOR 

To solve a problem like that on page loo, i.e., to find the quality 
after an adiabatic expansion from loo pounds absolute to 15 
pounds absolute, and the specific volume at the initial and final 
states, proceed as follows: 

From the curve of temperatures and pressures, select the tem- 
perature line which corresponds to 100 pounds and note where it 
cuts the saturation curve, because it is assumed that the steam is 
initially dry. The diagram gives the entropy as approximately 
1.6 1. Note the temperature line which cuts the temperature- 
pressure curve at 15 pounds, and estimate the value of x from its 
intersection with the entropy line 1.6 1; by this method the value 
of X is found to be about 0.89. In hke manner the volume may 
be estimated to be about 23.4 cubic feet. 

Temperature-Entropy Table. — Now that the computation of 
isoentropic changes has ceased to be the diversion of students 
of theoretical investigations and has become the necessity of 
engineers who are engaged in such matters as the design of 
steam-turbines, the somewhat inconvenient methods which were 
incapable of inverse solutions, have become somewhat burdei^- 
some. A remedy has been sought in the use of temperature- 
entropy diagrams just described. Such a diagram to be really 
useful in practice must be drawn on so large a scale as to be very 
inconvenient, and even then is liable to lack accuracy. To meet 
this condition of affairs a temperature- entropy table has been com- 
puted and added to the " Tables of the Properties of Saturated 
Steam." In this table each degree Fahrenheit from 180° to 430^ 
is entered together with the corresponding pressure. There 
have been computed and entered in the proper columns the 
following quantities, namely, quality x, heat contents xr + q, and 
specific volume v, for each hundredth of a unit of entropy. 

In the use of this table it is recommended to take the nearest 
degree of temperature corresponding to the absolute pressure 
if pressures are given. Following the line across the table select 
that column of entropy which corresponds most nearly with the 
initial condition; the corresponding initial volume may be read 
direc|ly. Follow down the entropy column to the lower temper- 



TEMPERATURE-ENTROPY TABLE 



107 



ature and then find the value of x and the specific volume. The 
external work for adiabatic expansion may now readily be found 
by aid of equation (120), page 102. As will appear later, the 
problems that arise in practice usually require the heat contents 
and not the intrinsic energy, so that property has been chosen 
in making up the table. 

For example, the nearest temperature to 100 pounds per square 
inch is 328° F.; the entropy column 1.59 gives for x, 0.995, which 
indicates half of one per cent of moisture in the steam. The corre- 
sponding volume is 4.39 cubic feet. The nearest temperature to 
15 pounds absolute is 213° F., and at 1.59 entropy the quality 
is 0.888 and the specific volume corresponding is 23.2 cubic 
feet. 

If greater accuracy is desired we must resort to interpolation. 
Usually it will be sufficient to interpolate between the lines for 
temperature in a given column of entropy, because the quantity 
that must be determined accurately is usually the dijjerence 

^/i + ?i — (^2^2 + ^2) 

and this difference for two given temperatures t^ and /g is very 
nearly the same if taken out of two adjacent entropy columns. 
A similar result will be found for the difference 

^iPl + ?1 — (^2P2 + ^2); 

if computed for values of x found in adjacent columns. 

Another way of looking at this matter is that one hundredth 
of a unit of entropy at 330 pounds corresponds to one per cent 
of moisture. 

Evidently this table can be used to solve problems in which 
the final volumes are given, or, as will appear later, to determine 
intermediate pressures for steam-turbines. 



Io8 SATURATED VAPOR 

EXAMPLES. 

1. Water at ioo° F. is fed to a boiler in which the pressure is 
1 20 pounds absolute per square inch. How much heat must 
be supplied to evaporate each pound? Ans. 11 18 b.t.u. 

2. One pound wet steam at 150 pounds absolute occupies 2.5 
cubic feet. What per cent of moisture is present ? What is the 
"quality" of the steam? Ans. 17.1 per cent of moisture x = 
.829. 

3. A pound of steam and water at 150 pounds pressure is 
0.6 steam. What is the increase of entropy above that of water at 
32° F. ? Ans. 1. 144. 

4. A kilogram of chloroform at 100° C. is 0.8 vapor. What is 
the increase of entropy above that of the liquid at 0° C. ? Ans. 
0.1959. 

5. The initial condition of a mixture of water and steam is 
/ = 320° ¥., X = 0.8. What is the final condition after adiabatic 
expansion to 212° F. ? Ans. 0.74. 

6. The initial condition of a mixture of steam and water is ^ = 
3000 mm., X = 0.9. Find the condition after an adiabatic expan- 
sion to 600 mm. Ans. 0.828. 

7. A cubic foot of a mixture of water and steam, x = 0.8, is 
under the pressure of 60 pounds by the gauge. Find its volume 
after it expands adiabatically till the pressure is reduced to 10 
pounds by the gauge; also the external work of expansion. Ans. 
2.68 cubic feet and 9980 foot-pounds. 

8. Three pounds of a mixture of steam and water at 120 
pounds absolute pressure occupy 4.5 cubic feet. How much 
heat must be added to double the volume at the same pressure, 
and what is the change of intrinsic energy? Ans. 1065 b.t.u.; 
750,400 foot-pounds. 

9. Find the intrinsic energy, heat contents and volume of 
5 pounds of a mixture of water and steam which is 80 per cent 
steam, the pressure being 150 pounds absolute. Ans. Intrinsic 
energy, 3,710,000; heat contents, 5095 b.t.u.; volume, 12. i cubic 
feet. 



TEMPERATURE-ENTROPY TABLE 



109 



10. Three pounds of water are heated from 60° F, and evapor- 
ated under 135.3 pounds gauge pressure. Find the heat added, 
and the changes in volume, and intrinsic energy. Ans. Heat 
added, 3490 b.t.u.; increase in volume, 8.99 cubic feet; intrinsic 
energy, 2,520,000. 

11. A pound of steam at 337^.7 F. and 100 pounds gauge 
pressure occupies 3 cubic feet. Find its intrinsic energy and its 
entropy above 32° F. Ans. Intrinsic energy, 718,000; entropy, 

1-336. 

12. Two pipes deliver water into a third. One supplies 300 
gallons per minute at 70° F. ; the other, 90 gallons per minute at 
200° F. What is the temperature of the water after the two 
streams unite? Ans. 100° F. 

13. Ten gallons of water per minute are to be heated from 
65° to 212° F. by passing through a coil surrounded by steam at 
120 pounds gauge pressure. How much steam is required per 
minute? Ans. 12 pounds. 

14. A test of an engine with the cut-off at 0.106 of the stroke, 
and the release at 0.98 of the stroke, and with 4.5 per cent clear- 
ance, gave for the pressure at cut-off 62.2 pounds by the indicator, 
and at release 6.2 pounds; the mixture in the cylinder at cut-off 
was 0.465 steam, and at release 0.921 steam. Find (i) condition 
of the mixture in the cylinder at release on the assumption of 
adiabatic expansion to release; (2) condition of mixture on the 
assumption of hyperbolic expansion, or that pv = piV^] (3) the 
exponent of an exponential curve passing through points of cut- 
off and release; (4) exponent of a curve passing through the initial 
and final points on the assumption of adiabatic expansion; (5) 
the piston displacement was 0.7 cubic feet, find the external work 
under exponential curve passing through the points of cut-off and 
release; also under the adiabatic curve. Ans. (i) 0.472; (2) 
0.524; (3) n = 0.6802; (4) n = 1.0589; (5) 3093 and 2120 foot- 
pounds. 



CHAPTER VII. 

SUPERHEATED VAPORS. 

A DRY and saturated vapor, not in contact with the liquid 
from which it is formed, may be heated to a temperature greater 
than that corresponding to the given pressure for the same 
vapor when saturated; such a vapor is said to be superheated. 
When far removed from the temperature of saturation, such a 
vapor follows the laws of perfect gases very nearly, but near the 
temperature of saturation the departure from those laws is too 
great to allow of calculations by them for engineering purposes. 

All the characteristic equations that have been proposed, 
have been derived from the equation 

pv = RT, 

which is very nearly true for the so-called perfect gases at mod- 
erate temperatures and pressures; it is, however, well known 
that the equation does not give satisfactory results at very high 
pressures or very low temperatures. To adapt this equation to 
represent superheated steam, a corrective term is added to the 
right-hand side, which may most conveniently be assumed to 
be a function of the temperature and pressure, so that calcula- 
tions by it may be made to join on to those for saturated steam. 

The most satisfactory characteristic equation of this sort is 
that given by Knoblauch,* Linde, and Klebe, 

pv = BT- p{i+ap)\c{^)'-D]^ . . (i2i) 

in it the pressure is in kilograms per square metre, v is in 
cubic metres, and T is the absolute temperature by the 

* MiUeilungen uher Forschungsarheiten, etc., Heft 21, S. TiZ^ 1905- 



SUPERHEATED VAPORS III 

centigrade thermometer. The constants have the following 
values : 

B = 47.10, a = 0.000002, C = 0.031, D = 0.0052. 

In the English system of units, the pressures being in pounds 
per square foot, the volumes in cubic feet per pound, and the 
temperatures on the Fahrenheit scale, we have 

pv=^.^s r-^(i +0.00000976^) ('-^^^^^°- 0.0833) (122) 

The following equation may be used with the pressure in 
pounds per square inch : 

pv=o.sg62 T~p (i +0.0014 P) r^°'^3^'^^^ -Q>o833J • (123) 

The labor of calculation is principally in reducing the cor- 
rective term, and especially in the computation of the factor 
containing the temperature. A table on page 112 gives values 
of this factor for each five degrees from 100° to 600° F.; the 
maximum error in the calculation of volume by aid of the table 
is about 0.4 of one per cent at 336 pounds pressure and 428° F.; 
that is at the upper limit of our table for saturated steam. At 
150 pounds and 358° F., which is about the middle range 
of our table for saturated steam, the error is not more than 0.2 
of one per cent, which is not greater than the probable error of 
the equation itself under those conditions. At lower pressures 
and at higher temperatures the error tends to diminish. 

The following simple equation is proposed by TumHrz * based 
on experiments by Battelli. 

pv = BT — Cp (124) 

where p is the pressure in kilograms per square metre, v the 
specific volume in cubic metres, and T the absolute temperature 
centigrade. The constants have the values 

B = 47.10 C = 0.016. 

* Math. Naturw. Kl. Wien,, 1899, Ha S. 1058. 



112 



SUPERHEATED VAPORS 



In the English system with the pressure in pounds per square 
foot and the volumes in cubic feet, for absolute temperatures 
Fahrenheit, 

pv = 85.85 T-0.2S6P (125) 

This equation has a maximum error of 0.8 of one per cent as 
compared with equation (121). 

TABLE I. 

-.T 1 r 1 f ii;o,^oo,ooo _ 

Values of the factor ' 0.0833. 



Temperature. 


Value 


Temperature. 


Value 


Temp 


>erature . 


Value 


Temperature. 


Value . 






of 






/-if 






/->f 






nf 






01 

Factor. 






01 
Factor. 






01 
Factor. 






01 

Factor. 


Fahr. 


Abs. 




Fahr. 


Abs. 




Fahr. 


Abs. 




Fahr. 


Abs. 




200 


659-5 


0.441 


300 


759-5 


0.260 


400 


859-5 


0.153 


500 


959-5 


0.087 


205 


664 


5 


0.429 


305 


764-5 


0.253 


405 


864 


5 


0.149 


505 


964.5 


0.084 


210 


669 


5 


0.417 


310 


769-5 


0.247 


410 


869 


5 


0.145 


510 


969-5 


0.083 


215 


674 


5 


0.405 


315 


774-5 


0. 240 


415 


874 


5 


0. 141 


515 


974-5 


0.079 


220 


679 


5 


0-395 


320 


779-5 


0.234 


420 


879 


5 


0.138 


520 


979-5 


0.077 


225 


684 


5 


0-385 


325 


784.5 


0.228 


425 


884 


5 


0.134 


525 


984.5 


0.074 


230 


689 


5 


0-375 


330 


789-5 


0.222 


430 


889 


5 


O.131 


530 


989-5 


0.072 


235 


694 


5 


0-365 


335 


794-5 


0.216 


■435 


894 


5 


0.127 


535 


994-5 


0.070 


240 


699 


5 


0-356 


340 


799.5 


0.2II 


440 


899 


5 


0.123 


540 


999-5 


0.067 


245 


704 


5 


0.347 


345 


804.5 


0.205 


445 


904 


5 


0. 120 


545 


T004.5 


0.065 


250 


709 


5 


0-338 


350 


809.5 


0. 200 


450 


909 


5 


0. 117 


550 


1009.5 


0.063 


255 


714 


5 


0.329 


355 


814.5 


0.195 


455 


914 


5 


O.I13 


555 


1014.5 


o.o6t 


260 


719 


5 


0.320 


360 


819.5 


0. 190 


460 


919 


5 


0. ITO 


560 


10T9.5 


0.059 


265 


724 


5 


0.312 


365 


824.5 


0.185 


465 


924 


5 


0. 107 


565 


1024.5 


0.057 


270 


729 


5 


0.304 


370 


829.5 


0. 180 


470 


929 


5 


0. 104 


570 


1029.5 


0.055 


275 


734 


5 


0.296 


375 


834.5 


0.175 


475 


934 


5 


0. lOI 


575 


1034.5 


0-053 


280 


739 


5 


0.288 


380 


839-5 


0. 171 


480 


939 


5 


0.098 


580 


1039-5 


0.051 


585 


744 


5 


0.281 


385 


844-5 


0.166 


485 


944 


5 


0.095 


585 


1044.5 


0.049 


290 


749 


5 


0.274 


390 


849.5 


0. 162 


490 


949 


5 


0.092 


590 


1049.5 


0.047 


295 


754-5 


0.267 


395 


854.5 


0.158 


495 


954-5 


0.090 


595 


1054.5 


0.045 



Specific Heat. — Two investigations have been made of the 
specific heat of superheated steam at constant pressure, one by 
Professor Knoblauch* and Dr. Jakob and the other by Pro- 
fessor Thomas and Mr. Short; f the results of the latter 's inves- 
tigation have been communicated for use in this book in 
anticipation of the publication of the completed report. 

* Mitteilungen uher Forschungsarheiten, Heft 36, p. 109. 
t Thesis by Mr. Short, Cornell University 



SPECIFIC HEAT 



113 



Professor Knoblauch's report gives the results of the inves- 
tigations made under his direction in the form of a table giving 
specific heats at various temperatures and pressures and in a 
diagram, which can be found in the original memoir, and he 
also gives a table of mean specific heats from the temperature of 
saturation to various temperatures at several pressures. This 
latter table is given here in both the metric system and in the 
English system of units. 

SPECIFIC HEAT OF SUPERHEATED STEAM. 

Knoblauch and Jakob 



/KgperSqCm 
p Lbs per Sq In. 

t» Cent. 

i$ Fahr. 


1 

14.2 

99° 
210° 


2 

28.4 
120° 
248° 


4 

56-9 
143° 
289° 


6 

85-3 
158° 

316^ 


8 

113. 8 
169° 
336° 


10 

142.2 

179° 
350° 


12 

170.6 
187° 
368° 


14 

199. 1 

194° 
381° 


16 

227.5 
200° 
392° 


18 

156.0 
206° 
403° 


20 

284.4 
211° 
412° 


Fahr. 
212° 
302° 
392° 
482° 

572° 
662° 

752° 


Cent. 

100° 
150° 
200° 
250° 
300° 
350° 
400° 


0.463 
0.462 
0.462 
0.463 
0.464 
0.468 
0-473 


o.'478 

0-475 
0.474 

0-475 
0.477 
0.481 


0-515 
0. 502 

0-495 
0.492 
0.492 
0.494 


0-530 
0.514 

0-505 
0.503 
0.504 


0.560 
0.532 
0.517 
0.512 
0.512 








597 
552 
530 
522 
520 


0.635 
0.570 
0.541 

0.529 
0. 526 


0.677 
0.588 
0.550 
0.536 
0-531 








609 
561 

543 
537 








635 
572 

550 
542 








664 

585 

557 
547 



The construction of this table is readily understood from the 
following example: — Required the heat needed to superheat a 
kilogram of steam at 4 kilograms per square centimetre from 
saturation to 300° C. The saturation temperature (to the nearest 
degree) is 143° C; so that the steam at 300° is superheated 157°, 
and for this is required the heat 

157 X 0.492 = 77.2 calories. 

The experiments of Professor Knoblauch were made at 2, 4, 
6, and 8 kilograms per square centimetre; the remainder of the 
table was obtained from the diagram which was extended by aid 
of cross- curves to the extent indicated. Within the limits of 
the experimental work the table may be used with confidence. 
Exterpolated results are probably less reliable than those 
obtained directly by Professor Thomas. 



114 



SUPERHEATED VAPORS 



The following table gives the mean specific heat of super- 
heated steam as measured on a facsimile of Professor Thomas's 
original diagram without exterpolation. 



SPECIFIC HEAT OF SUPERHEATED STEAM 

Thomas and Short. 







Pressure Lbs 


. per Sq. In 


(Absolute.) 




Degrees of 
Superheat Fahr. 
































6 


15 


30 


50 


100 


200 


400 


20° 


0-536 


0-547 


0.558 


0.571 


0.593 


0.621 


0.649 


50° 


0.522 





532 


0.542 


0.555 


0.575* 


0.600 


0.621 


100° 


o-S^Z 





512 


0.524 


0.537 


0.557 


0.581 


0.599 


150° 


0.486 





496 


0.508 


0.522 


0.544 


0.567 


0.585 


200° 


0.471 





480 


0.494 


0.509 


0.533 


0.556 


0.574 


250° 


0.456 





466 


0.481 


0.496 


0.522 


0.546 


0.564 


300° 


0.442 


0-453 


0.468 


0.484 


0.511 


0.537 


0.554 



Here again the arrangement of the table can be made evident 
by an example : — Required the heat needed to superheat steam 
100 degrees at 200 pounds per square inch absolute. The mean 
specific heat from saturation is 0.581, so that the heat required 
is 58.1 thermal units. 

Total Heat. — In the solution of problems that arise in engi- 
neering it is convenient to use the total amount of heat required 
to raise one pound of water from freezing-point to the tempera- 
ture of saturated steam at the given pressure and to vaporize 
it and to superheat it at that pressure to the given temperature. 
This total heat may be represented by the expression 



H 



Sup. 



r + c^ {t— ts) 



where / is the superheated temperature of the superheated 
steam, 4 is the temperature of saturated steam at the given 
pressure p, and q and r are the corresponding heat of the liquid 
and heat of vaporization. The mean specific heat Cp may 
usually be selected from one of the given tables without inter- 



ENTROPY 



115 



polation, as a .small variation does not have a very large 
effect. 

The total heat or heat contents of superheated steam in the 
temperature- entropy table were obtained by the following 
method. From Professor Thomas's diagram giving mean 
specific heats, curves of specific heats at various temperatures 
and at a given pressure were obtained, and the curves thus 
obtained were faired after a comparison with curves constructed 
with Professor Knoblauch 's specific heats at those temperatures. 
These curves were then integrated graphically and the results 
checked by comparison with his mean specific heats. 

Entropy. — By the entropy of superheated steam is meant 
the increase of entropy due to heating water from freezing-point 
to the temperature of saturated steam at the given pressure, to 
the vaporization and to the superheating at that pressure. This 
operation may be represented as follows: 






^ cpdt 



in which T is the absolute temperature of the superheated steam, 
and Ts is the temperature of the saturated steam at the given 

pressure; and— maybe taken from the '^ Tables of Saturated 

Steam." The last term was obtained for the temperature- 
entropy table by graphical integration of curves plotted 

with values of -£^ derived from the curves of specific heats at 

various temperatures just described under the previous section. 

If the temperature- entropy table is not at hand, the last term 
of the above expression may be obtained approximately by divid- 
ing the heat of superheating, by the mean absolute temperature 
of superheating. 

This may be expressed as follows: 



h (t- t,) + 459-5 



Il6 SUPERHEATED VAPORS 

where / is the temperature of the superheated steam, 4 is the 
temperature of saturated steam at the given pressure, and Cp is 
the mean specific heat of superheated steam. 

If this method is considered to be too crude, the computation 
can be broken into two or more parts. Thus if t^ is an inter- 
mediate temperature, the increase of entropy due to superheat- 
ing may be computed as follows: 

^ {h - is) + 459-5 2 {t - h) + 459-5 

where cj is the mean specific heat between 4 and /^ and c/' is 
the specific heat between 4 and /. This method may evidently 
be extended to take in two intermediate temperatures and give 
three terms. 

Adiabatic Expansion. — The treatment of superheated steam 
in this chapter resembles that for saturated steam in that it does 
not yield an explicit equation for the adiabatic line. If the 
steam were strongly superheated during the whole operation it 
is probable that the adiabatic line would be well represented 
by an exponential equation, and for such case a mean value of 
the exponent could be determined that would suffice for engi- 
neering work. But even with strongly superheated steam at 
the initial condition the final condition is likely to show moisture 
in the steam after adiabatic expansion, or, for that matter, after 
expansion of the steam in the cylinder of an engine or in a steam- 
turbine. 

Problems involving adiabatic expansion of steam which is 
initially superheated can be solved by an extension of the method 
for saturated steam, and this method applies with equal facility 
to problems in which the steam becomes moist during the expan- 
sion. The most ready method of solution is by aid of the tempera- 
ture-entropy table, which may be entered at the proper pressure 
(or the corresponding temperature of saturated steam) and the 
proper superheated temperature, it being in practice sufficient to 
take the line for the nearest tabular pressure and the column 



PROPERTIES OF SULPHUR DIOXIDE I17 

showing the nearest degree of superheating. Following down 
the column for entropy to the final pressure, the properties for 
the final condition will be found; these will be the heat con- 
tents, specific volume, and either the temperature of superheated 
steam or the quality x, depending on whether the steam remains 
superheated during the expansion or becomes moist. 

If the external work of adiabatic expansion of steam initially 
superheated is desired, it can be had by taking the difference of 
the intrinsic energies. The heat equivalent of intrinsic energy 
of moist steam is 

xp -\- q = X (r — Apu) -{- q = xr -{- q — Apxu^ 

and of this expression the quantity xr + q may be taken from 
the temperature- entropy table, and the quantity Apxu can 
be determined by aid of the steam table. In like manner the 
heat contents of superheated steam 



/ 



cjt 



which is computed and set down in the temperature- entropy 
table may be made to yield the heat equivalent of the intrinsic 
energy by subtracting the heat equivalent of the external work 
of vaporizing and superheating the steam 

Ap {v- 0-), 

where v is the specific volume of the superheated steam. This 
method is subject to some criticism, especially when the steam 
is not highly superheated, because some heat will be required 
to do the disgregation work of superheating. Fortunately the 
greater part of problems arising in engineering involve the heat 
contents, so that this question is avoided. 

Properties of Sulphur Dioxide. — One of the most interesting 
and important applications of the theory of superheated vapors 
is found in the approximate calculation of properties of certain 
volatile liquids which are used in refrigerating- machines, and for 
which we have not sufficient experimental data to construct tables 
in the manner explained in the chapter on saturated vapors. 



Il8 SUPERHEATED VAPORS 

For example, Regnaulf made experiments on the pressures 
of saturated sulphur dioxide and ammonia, but did not de- 
termine the heat of the Kquid nor the total heat. He did, 
however, determine some of the properties of these substances 
in the gaseous or superheated condition, from which it is pos- 
sible to] construct the characteristic equations for the super- 
heated vapors. These equations can then be used to make 
approximate calculations of the saturated vapors, for such equa- 
tions are assumed to be appHcable down to the saturated con- 
dition. Of course such calculations are subject to a considerable 
unknown error, since the experimental data are barely sufficient 
to establish the equations for the superheated vapors. 

The specific heat of gaseous sulphur dioxide is given by 
Regnault * as 0.15438, and the coefficient of dilatation as 
0.0039028. The theoretical specific gravity compared with air, 
calculated from the chemical composition, is given by Landolt 
and Bornstein f as 2.21295. Gmelin J gives the following 
experimental determinations: by Thomson, 2.222; by Berzelius, 
2.247. The figure 2.23 will be assumed in this work, which 
gives for the specific volume at freezing-point and at atmospheric 
pressure 

y = '' ''^'^ = 0.347 cubic metres. 
2.23 

The corresponding pressure and temperature are 10,333 ^^^ 
273° c. 

At this stage it is necessary to assign a probable form for the 
characteristic equation, and for that purpose the form 

pv = BT - Cp"" (125) 

proposed by Zeuner has commonly been used, and it is con- 
venient to admit that it may take the form 

pv = -^aT- Cp^ (126) 

* Memoir es de VInstitut de France, tome xxi, xxvi. 
t Physikalische-chemische Tabellen. 
% Watt's translation, p. 280. 



PROPERTIES OF SULPHUR DIOXIDE II9 

The value of the arbitrary constant a may be determined 
from the coefficient of dilatation as follows. The coefficient 
of dilatation is the ratio of the increase of volume at constant 
pressure, for one degree increase of temperature, to the original 
volume; so that the preceding equation applied at 0° C. and at 
1° C. gives f 

p,v, = ^aT,- Cpo^; 



The value of a obtained by substituting known values in the 
above equation is 0.212. Now as a appears in both the first and 
the last terms of the right-hand side of equation (126), a con- 
siderable change in a has but little effect on the computations 
by aid of that equation. As will appear later an assumption 
of a value 0.22 for a will make equation (126) agree well with 
certain experiments on the compressibility of sulphur dioxide, 
and it will consequently be chosen. If now we reverse the process 
by which a was calculated from the coefficient of dilatation, 
the latter constant will appear to have a computed value of 
0.004, which is but little different from the experimental value. 

To compute C we have 

0.15438 X 426.9 X 0.22 = 14.5, 
and the coefficient of p"" is 

14.5 X 273 - 10333 X 0.347 ^ ^8 ^,^,ly. 

10333 

so that the equation becomes 

pv= 14.5^-48/-^^ ..... (127) 
Regnault found for the pressures 

p^ = 697.83 mm. of mercury, 
p2 = 1341.58 mm. of mercury, 
and at 7°. 7 C. the ratio 

^=1.02088. 



I20 SUPERHEATED VAPORS 

Reducing the given pressures to kilograms on the square 
metre, and the temperature to the absolute scale, and applying 
to equation (127), we obtain 1.016 instead of the experimental 
value for the above ratio. 

Regnault gives for the pressure of saturated sulphur dioxide, 
in mm. of mercury, the equation 

logp = a — ha"" — c/T; 

a = 5.6663790; 
logb = 0.4792425; 
logc = 9.1659562 — 10; 
log a = 9.9972989 — 10; 
log /? = 9.98729002 — 10; 

w = / + 28° c. 
Applying equation (95), page 76, to this case, 

ijA^Aa' + BlT; 
p at 

log a = 9.9972989; 

log /? =^ 9.98729002; 

log^ -= 8.6352146; 

log^ = 7.9945332; 

n = t + 28° C. 

The specific volume of saturated sulphur dioxide may be 
calculated by inserting in equation (127) for the superheated 
vapor the pressures calculated by aid of the above equation. 
The results at several temperatures are as follows: 

/ — 30° C. o + 30° C. 

5 0.8292 0.2256 0.0825 

Andreeff * gives for the specific gravity of fluid sulphur dioxide 
1.4336; consequently the specific volume of the liquid is 

o" = 0.0007. 

* Ann. Chem. Pharm., 1859. 



PROPERTIES OF SULPHUR DIOXIDE 121 

The value of r, the heat of vaporization, may now be calcu- 
lated at the given temperatures by equation (106), page 89, 

dt 
in which it = s — o". 

The results are 

/ - 30° C. o + 30° C. 

r 106.9 97.60 90.54 

Within the limits of error of our method of calculation, the 
value of r may be found by the equation 

r = 98 — 0.27 t (128) 

The specific heat of the liquid is derived by the following 
device. First assume that the entropy of the superheated vapor 
may be calculated by the equation 

T p 

given on page 67 for perfect gases. This may be transformed 

dcl> = c,[^---^-dp) .... (129) 

But if we introduce into the equation for a perfect gas 

pv = RT, 
the value of R from the equation 

Cp — c^ = AR, 

the characteristic equation may take the form 

Cpic — I 

pv = ^ T- 

^ A It 

Comparison of this equation with equation (126) suggests 

ic — I 
replacing the term in equation (129) by the arbitrary 

factor a, so that it may read 

d4> - Cj,[-^ - a-dp^ . . . . . (130) 



122 SUPERHEATED VAPORS 

The expression for the entropy of a Uquid and its vapor is 

XT Y I 

-=- + ^ or -- + I cdt 
T T J 

if the vapor is dry. When differentiated this yields 

d^ ^ ~ ^cdt -h dr - j^dt^ . . . .(131) 

If it be assumed that equations (130) and (131) may both be 
appHed at saturation v^^e have 

/ Tdp\ ^ dr r , . 

'^['~''-p-dt)=='^-di~T ' • ■ ^'^'^ 

If it be admitted further that the differential coefhcient -7- can 

dt 

be computed by the equation on page 120, the above equation 
affords a means of estimating the specific heat of the liquid. At 
0° C, this method gives for the specific heat 

c = 0.4. 
In English units v^e have for superheated sulphur dioxide 

pv=^ 26.4T-1S4P'-'' (133) 

the pressures being in pounds on the square foot, the volumes 
in cubic feet, and the temperatures in Fahrenheit degrees 
absolute. 

For pressures in pounds on the square inch at temperatures 
on the Fahrenheit scale, 

logp = a— ha'' — c/?"; 

^ = 3-9527847; 
log h = 0.4792425; 
log c = 9.1659562 — 10; 
log a = 9.9984994 — 10; 
log /? = 9.99293890 — 10; 

n = t + i8°.4 F. 



PROPERTIES OF AMMONIA 



123 



For the heat of vaporization 

r = 176 — 0.27 (/ — 32) (134) 

and for the specific heat of the Hquid 

c = 0.4. 

. In applying these equations to the calculation of a table of 
the properties of saturated sulphur dioxide the pressures corre- 
sponding to the temperatures are calculated as usual. Then 
the heat of the liquid is calculated by aid of the constant specific 
heat. The heat of vaporization is calculated by aid of equation 
(134). Next the specific volume is calculated by inserting the 
given temperature and the corresponding pressure for the sat- 
urated vapor in the characteristic equation (133). Having 
the specific volume of the vapor and that of the liquid, the heat 
equivalent (Apu) of the external work is readily found. Finally, 
the entropy of the liquid is calculated by the equation 

rp 

. 0= doge— (135) 

^ 

If the reader should object that this method is tortuous and 
full of doubtful approximations and assumptions, he must bear 
in mind that any method that can give approximations is better 
than none, and that all the computations for refrigerating- 
machines, that use volatile fluids, depend on results so obtained. 
And further, much of the waste and disappointment of earlier 
refrigerating- machines could have been avoided if tables as good 
as those computed by this method were then available. 

Properties of Ammonia. — The specific heat of gaseous 
ammonia, determined by Regnault, is 0.50836. The theoretical 
specific gravity compared with air, calculated from the chemical 
composition, is given by Landolt and Bornstein as 0.58890. 
Gmelin gives the following experimental determinations: by 
Thomson, 0.5931; by Biot and Arago, 0.5967. For this work 
the figure 0.597 will be assumed, which gives for the specific 
volume at freezing-point and at atmospheric pressure 

^ ^ '1166 = J c?o cubic metres. 
0-597 



124 SUPERHEATED VAPORS 

The coefficient of dilatation has not been determined, and con- 
sequently cannot be used to determine the value of a in equation 
(126). It, however, appears that consistent results are obtained 
if a is assumed to be \. The coefficient of T then becomes 

0.50836 X 426.9 X i = 54-3^ 

and the coefficient of p^ is 

54.3 X 273 - 10333 X 1.30 . 

. J-4^> 

10333 

SO that the equation becomes 

P'^ = 54-3 T —\\2 p^ (136) 

The coefficient of dilatation, calculated by the same process 
as was used in determining a for sulphur dioxide, is 0.00404, 
which may be compared with that for sulphur dioxide. 

Regnault found for the pressures 

P\ = 703.50 mm. of mercury, 
^2 = 1435-3 rnin- of mercury, 

and at 8°.i'C. the ratio 

^^^1.0188, 

while equation (136) gives under the same conditions 1.0200. 
For saturated ammonia Regnault gives the equation 

log^ = a — haJ" — c/T; 

a = 11.5043330; 
log h = 0.8721769; 
log c = 9.9777087 — 10; 
log a = 9.9996014 — 10; 
log /? = 9.9939729 — 10; 

^ - / + 22° C; 



PROPERTIES OF AMMONIA 



125 



by aid of which the pressures in mm. of mercury may be calculated 
for temperatures on the centigrade scale. The differential 
coefficient may be calculated by aid of the equation 

p at 
log A = 8.1635170 — 10; 
log 5 = 8.4822485 — 10; 
log a = 9.9996014 — 10; 
log /? = 9.9939729 - 10; 
n = / + 22° C. 

The specific volume of saturated ammonia calculated by 
equation (136) at several temperatures are 

/ — 30° C. o + 30° C 

s 0.9982 0.2961 0.1167 

Andreeff gives for*1ftie specific gravity of liquid ammonia at 
0° C. 0.6364, so that the specific volume of the Hquid is 

(T = 0.0016. 

The values of r at the several given temperatures, calculated 
by equation (128), are 

/ - 30° C. o + 3o°C. 

^ 325-7 300-15 277.5 

which may be represented by the equation 
r = 300 — 0.8 /. 

The specific heat of the liquid, calculated by aid of equation 

(132), is 

C = I.I. 

In Enghsh units the properties of superheated or gaseous 
ammonia may be represented by the equation 

pv = gg T — 710 p^, 

in which the pressures are taken in pounds on the square foot 
and volumes in cubic feet, while T represents the absolute 
temperature in Fahrenheit degrees. 



126 SUPERHEATED VAPORS 

I'he pressure in pounds on the square inch may be calculated 
by the equation 

log^ = a'— ba" — c^"", 

a = 9.7907380; 
log b = 0.8721769 — 10; 
log c - 9.9777087 — 10; 
log a = 9.9997786 — 10; 
log /? = 9.9966516 — 10; 
n = t + 7° 6 F. 

The heat of vaporization may be calculated by the equation 
r = 540 - 0.8 (/- 32), 
and the specific heat of the hquid is 

C = I.I. 

m 

EXAMPLES. 

1. What is the weight of one cubic foot of superheated steam 
at 500° F. and at 60 pounds pressure absolute? Knoblauch's 
equation. Ans. 0.106 pounds. 

2. Superheated steam at 50 pounds absolute has half the 
density of saturated steam at the same pressure. What is the 
temperature? Tumlirz's equation. Ans. 930° F. 

3. What is the volume of 5 pounds of steam at 129.3 pounds 
gauge pressure and at 359^.5 F. ? Ans. 15.8. 

4. At 129.3 pounds gauge pressure 2 pounds of steam occupy 
7 cubic feet. Find its temperature. Assume value of T for 
entering Table I, page 112, and solve by trial. Ans. 424° F. 

5. A cubic foot of steam at 140 pounds absolute weighs 0.30 
pounds. What is its temperature? Ans. 374*^ F. 

6. Two pounds of steam and water at 129.3 pounds pressure 
above the atmosphere occupy 6 cubic feet. Heat is added and 
the pressure kept constant till the volume is 8.5 cubic feet. Find 
the final condition, and the external work done in expanding. 
Ans. Temperature 681° F.; work 51800. 



EXAMPLES 



127 



7. Saturated steam at 150 pounds gauge, containing 2 per cent 
of water, passes through a superheater on its way to an engine. 
Its final temperature is 400° F. Find the increase in volume 
and the heat added per pound. 

8. Let the initial temperature of superheated steam be 380° F. 
at the pressure of 150 pounds absolute. Find the condition 
after an adiabatic expansion to 20 pounds absolute. Determine 
also the initial and final volumes. Ans. (i) 0.895; (2) 3.09 
cubic feet; (3) 17.8 cubic feet. 

9. In example 9, page 109, suppose that the steam at cut-ofi" 
were superheated 10° F. above the temperature of saturated 
steam at the given pressure, and solve the example. Ans. 
(i) 0.887; (2) 87° superheating; (3) same as before; (4) n = 
i-i37> (5) 1972 and 1950 foot-pounds. 



CHAPTER VIII. 

THE STEAM-ENGINE. 

The steam-engine is still the most important heat-engine, 
though its supremacy is threatened on one hand by the steam- 
turbine and on the other by the gas-engine. When of large size 
and properly designed and managed its economy is excellent and 
can be excelled only by the largest and best gas-engines, 
and in many cases these engines (even with the advantage of 
a more favorable range of temperature) depend for their com- 
mercial success on the utilization of by-products. 

It can be controlled, regulated, and reversed easily and posi- 
tively — properties which are not possessed in like degree by 
other heat-engines. It is interesting to know that the theory 
of thermodynamics was developed mainly to account for the 
action and to provide methods of designing steam-engines; 
though neither object is entirely accomplished, on account of 
the fact that the engine-cylinder must be made of some metal to 
be hard and strong enough to endure service, for all metals are 
good conductors of heat, and seriously affect the action of a con- 
densable fluid like steam. 

Carnot^s Cycle for a steam-engine is repre- 
sented by Fig. 31, in which ah and cd are 
isothermal lines, representing the application 
and rejection of heat at constant temperature 
and at constant pressure, he and da are 
adiabatic lines, representing change of tem- 
perature and pressure, without transmission 




^^'^^' of heat through the walls of the cyhnder. 

The diagram representing Carnot 's cycle has an external resem- 
blance to the indicator-diagram from some actual engines, 
but it differs in essential particulars. 

128 



CARNOT'S CYCLE 



129 



In the condition represented by the point a the cylinder con- 
tains a mixture of water and steam at the temperature /^ and 
the pressure p^. If connection is made with a source of heat 
at the temperature t^, and heat is added, some of the water will 
be vaporized and the volume will increase at constant pressure 
as represented by ab. If thermal communication is now inter- 
rupted, adiabatic expansion may take place as represented by be 
till the temperature is reduced to t2, the temperature of the 
refrigerator, with which thermal communication may now be 
established.. If the piston is forced toward the closed end of 
the cylinder some of the steam in it will be condensed, and the 
volume will be reduced at constant pressure as represented by 
cd. The cycle is completed by an adiabatic compression rep- 
resented by da. 

If the absolute temperature of the source of heat is T^, and 
if that of the refrigerator is T^, then the efficiency is 

, - r. - r. 

whatever may be the working fluid. 

For example, if the pressure of the steam during isothermal 
expansion is 100 pounds above the atmosphere, and if the pressure 
during isothermal compression is equal to that of the atmos- 
phere, then the temperatures of the source of heat and of the 
refrigerator are 337°.6 F. and 212° F., or 797.1 and 671.5 abso- 
lute, so that the efficiencv is 



707.1 — 671. c; 

^^ —^^= 0.157. 

797-1 



The following table gives the efficiencies worked out in , a 
similar way, for various steam- pressures, — both for t^ equal to 
212° F., corresponding to atmospheric pressure, and for t^, 
equal to 116° F., corresponding to an absolute pressure of 1.5 
pounds to the square inch: 



I30 



THE STEAM-ENGINE 



EFFICIENCY OF CARNOT'S CYCLE FOR STEAM-ENGINES. 



Initial Pressure 
by the Gauge, 

above the 
Atmosphere. 


Atmospheric 
Pressure. 


i.S Pounds 
Absolute. 


15 
30 


0-053 
0.084 


0.189 
0.215 


60 


0. 124 


0.249 


100 


o»i57 


0.278 


150 


0.186 


0.302 


200 


0,207 


0.320 


300 


0.238 


0-347 



The column for atmospheric pressure may be used as a 
standard of comparison for non-condensing engines, and the 
column for 1.5 pounds absolute may be used for condensing 
engines. 

It is interesting to consider the condition of the fluid in the 
cylinder at the different points of the diagram for Carnot's 
cycle. Thus if the fluid at the condition represented by b in 
Fig. 31 is made up of x^ part steam and i—Xf, part water, then 
from equation (118) the condition at the point c is given by 

^. = ^(^% + ^.-^.) • • • • (137) 



In like manner the condition of the mixture at the point d is 



^d 



(|^ x„ + e,- e,j .... (138) 



It is interesting to note that if Xf, is larger than one-half, that 
is, if there is more steam than water in the cylinder at ft, then 
the adiabatic expansion is accompanied by condensation. Again, 
if Xa is less than one-half, then the adiabatic compression is also 
accompanied by condensation. Very commonly it is assumed 
that Xb is unity, so that there is dry saturated steam in the cylin- 
der at b\ and that Xa is zero, so that there is water only in the 



EFFICIENCY OF CARNOT'S CYCLE 



131 



P60 



cylinder at a; but there is no necessity for such assumptions, 
and they in no way affect the efficiency. 

The temperature-entropy diagram for Carnot's cycle for a 
steam-engine is shown by Fig. 32, on which are drawn also the 
lines for entropy of the liquid 
mdj and the entropy of satur- 
ated vapor bCy as well as the 
lines which represent the value 
of Xy the dryness factor. This 
diagram represents to the eye 
the vaporization during the 
isothermal expansion ab, the 
partial condensation during 
the adiabatic expansion be, 
the isothermal condensation 




0.1 0.2 0.3 



¥ 



Fig. 32. 

along cdj and the condensation 
during the adiabatic compression da. In the diagram the work- 
ing substance is shown as water at a and as dry steam at b; 
the efficiency would clearly be the same for a cycle a' y c' d' , 
which contains a varying mixture of water and steam under all 
conditions. 

If the cylinder contains M pounds of steam and water, the 
heat absorbed by the working substance during isothermal 
expansion is 

Q^ = Mr^ {^x^ - x„) , (139) 

and the heat rejected during isothermal compression is 

so that the heat changed into work during the cycle is 
Qi - Q^ = M\r^ {Xf, - Xa) - r^ (x^ - Xa)l 



But from equations (137) and (138) 



-^ 1 



132 



THE STEAM-ENGINE 



and the expression for the heat changed into work becomes 

Q^-Q2- Mr, (x, - xj ^1 ~ ^' . . . (140) 

^ 1 

This equation is deduced because it is convenient for making 
comparisons of various other volatile liquids and their vapors, 
with steam, for use in heat-engines. It is of course apparent 



from equations (139) and (140), a conclusion which is known 
independently, and indeed is necessary in the development of 
the theory of the adiabatic expansion of steam. 

In the discussion thus far it has been assumed that the work- 
ing fluid is steam, or a mixture of steam and water. But a 
mixture of any volatile liquid and its vapor will give similar 
results, and the equations deduced can be applied directly. The 
principal difference will be due to the properties of the vapor 
considered, especially its specific pressures and specific volumes 
for the temperatures of the source of heat and the refrigerator. 

For example, the efficiency of Carnot's cycle for a fluid 
working between the temperatures 160° C. and 40° C. is 

160 — 40 

— =^— = 0.277. 

160 + 273 

The properties of steam and of chloroform at these tempera- 
tures are 

Pressure, mm. mercury 
Volume, cubic metres . 
Heat of vaporization, r 
Entropy of liquid, . . 

For simplicity, we may assume that one kilogram of the fluid 
is used in the cylinder for Carnot's cycle, and that Xi, is unity 
while Xa is zero, so that from equation (140) 

T - T 



Steam 




Chloroform. 


40° c. 


160° c. 


4o°C. 160° C. 


54.91 


4651.4 


369.26 8734.2 


19.74 


0-3035 


0.4449 0.0243 


78.7 


494.2 


63-13 50.53 


0.1364 


0.4633 


0.03196 O.IIO41 



r. 



EFFICIENCY OF CARNOT'S CYCLE 133 

and for steam 

Qi - Q2 == 494-2 X 0.277 = 137 calories, 
while for chloroform 

Qi - Q2= 50-53 X 0.277 = 14 calories. 

After adiabatic expansion the qualities of the fluid will be, 
from equation (137), for steam 

and for chloroform 

Xr = — ^ I 5_Oj _|. 0.IIO4I — 0.0^106) = 0.060. 

63.13 U60 + 273 4 5 y / y y 

The specific volumes after adiabatic expansion are, conse- 
quently, for steam 

v^ = XcU^ + o" = 0.795 (19.74 — o.ooi) + o.ooi = 15.7, 

and for chloroform 

Vc = x^u^ + o" = 0.969 (0.4449 — 0.000655) + 0.000655 = 0.431. 

These values for v^ just calculated are the volumes in the 
cylinder at the extreme displacement of the piston, on the 
assumption that one kilogram of the working fluid is vaporized 
during isothermal expansion. A better idea of the relative 
advantages of the two fluids will be obtained by finding the 
heat changed into work for each cubic metre of maximum piston- 
displacement, or for a cylinder having the volume of one cubic 
metre. This is obtained by dividing Q^ — Q^, the heat changed 
into work for each kilogram by v^. For steam the result is 

(Qi - Q2) -^ ^c = 137 - 15-7 == 8.73, 

and for chloroform it is 

(Qi - Q2) - ^^c =- 14 -^ 0.413 = 34; 
from which it appears that for the same volume chloroform 
can produce more than three and a half times as much power. 



134 



THE STEAM-ENGINE 



Even if we consider that the difference of pressure for chloro- 
form, 

8734.2 - 369.3 = 8364.9 mm., 

is nearly twice that for steam, which has only 
4651:4 - 54.9 = 4596.5 mm. 

difference of pressure, the advantage appears to be in ; favor of 
chloroform. If, however, the difference of pressures given for 
chloroform is allowable also for steam, giving 

8364.9 + 54.9 = 8419.8 mm. 

for the superior pressure, then the initial temperature for steam 
becomes 184^.9 C-> ^^^ ^^^ efficiency becomes 

184.9 "-40 o 

— ^ =0.^18, 

184.9 +273 

instead of 0.277. On the whole, steam is the more desirable 
fluid, even if we do not consider the inflammable and poisonous 
nature of chloroform. Similar calculations will show that on 
the whole steam is at least as well adapted for use in heat-engines 
as any other saturated fluid; in practice, the cheapness and 
incombustibility of steam indicate that it is the preferable fluid 
for such uses. 

Non-conducting Engine. Rankine Cycle. — The conditions 
required for alternate isothermal expansion and adiabatic expan- 
sion cannot be fulfilled for Carnot's cycle with steam any more 
than they could be for air. The diagram for the cycle with 
steam, however, is well adapted to production of power; the 
contrary is the case with air, as has already been shown. 

In practice steam from a boiler is admitted to the cylinder of 
the steam-engine during that part of the cycle which corre- 
sponds to the isothermal expansion of Carnot 's cycle, thus, trans- 
ferring the isothermal expansion to the boiler, where steam is 
formed under constant pressure. In like manner the isothermal 
compression is replaced by an exhaust at constant pressure, 
during which steam may be condensed in a separate condenser, 



a 

V 









NON-CONDUCTING ENGINE 135 

cooled by cold water. The cylinder is commonly made of cast 
iron, and is always some kind of metal; there is consequently 
considerable interference due to the conductivity of, the walls of 
the cylinder, and the expansion and compression are never 
adiabatic. There is an advantage, however, in discussing first 
an engine with a cylinder made of some non-conducting material, 
although no such material proper for making cylinders is now 
known. 

The diagram representing the operations in a non-conducting 
cylinder for a steam-engine (sometinies called the Rankine cycle) 
can be represented by Fig. 33. ab represents 
the admission of dry saturated steam from 
the boiler; be is an adiabatic expansion to the 
exhaust pressure; cd represents the exhaust; 
and da is an adiabatic compression to the ''"' fig. 33. 
initial pressure. It is assumed that the small 
volume, represented by a, between the piston and the head of 
the cylinder is filled with dry steam, and that the steam remains 
homogeneous during exhaust so that the quality is the same at 
d as at c. These conditions are consistent and necessary, 
since the change of condition due to adiabatic expansion (or 
compression) depends only on the initial condition and the 
initial and final pressures; so that an adiabatic expansion from 
a to d would give the same quality at ^ as that found at c after 
adiabatic expansion from b, and conversely adiabatic compres- 
sion from d to a gives dry steam at a as required. 

The cycle represented by Fig. 33 differs most notably from 
Carnot's cycle (Fig. 32) in that ab represents admission of steam 
and cd represents exhaust of steam, as has already been pointed 
out. It also differs in that the compression da gives dry steam 
instead of wet steam. The compression line da is therefore 
steeper than for Carnot's cycle, and the area of the figure is 
slightly larger on this account. This curious fact does not 
indicate that the cycle has a higher efficiency; on the contrary, 
the efficiency is less, and the cycle is irreversible. 

If the pressure during admission (equal to the pressure in 



136 THE STEAM-ENGINE 

the boiler) is p^, and if the pressure during exhaust is p^j then 
the heat required to raise the water resuhing from the conden- 
sation of the exhaust-steam is 

where q^ is the heat of the Uquid at the pressure p^y and q^ is the 
heat of the Uquid at the pressure p^. The heat of vaporization 
at the pressure p^ is r^, so that the heat required to raise the feed- 
water from the temperature of the exhaust to the temperature 
in the boiler and evaporate it into dry steam is 

Oi = ^ +?i - ?2 (141) 

and this is the quantity of heat supplied to the cylinder per 
pound of steam. 

The steam exhausted from the cylinder has the quality x^y 
calculated by aid of the equation 

and the heat that must be withdrawn when it is condensed is 

Q2 = ^2^ (142) 

this is the heat rejected from the engine. The heat changed 
into work per pound of steam is 

<3i - 62 = ^1 + ?i - ?2 - ^2^2 . . . • (143) 

The efficiency of the cycle is 

If values are assigned to p^ and p^ and the proper numerical 
calculations are made, it will appear that the efficiency for a 
non-conducting engine is always less than the efficiency for 
Carnot's cycle between the corresponding temperatures. 

It should be remarked that the efficiency is not affected by 
the clearance or space between the piston and the head of the 
cylinder and the space in the steam-passages of the cylinder, 
provided that the clearance is filled with dry saturated steam as 



USE OF THE TEMPERATURE-ENTROPY DIAGRAM 



137 



indicated in Fig. t,2>' This is evident from the fact that no term 
representing the clearance, or volume at a, Fig. 33, appears in 
equation (144). Or, again, we may consider that the steam in 
the cylinder at the beginning of the stroke, occupying the vol- 
ume represented by a, expands during the adiabatic expansion 
and is compressed again during compression, so that one 
operation is equivalent to and counterbalances the other, and 
so does not affect the efficiency of the cycle. 

Use of the Temperature-Entropy Diagram. — The Rankine 
cycle is drawn with a varying quantity of steam in the cylinder, 
beginning at a, Fig. 33, with the steam caught in the clearance 
and finishing at b, with that weight plus the weight drawn from 
the boiler; consequently a proper temperature-entropy diagram, 
which represents the changes of one pound of the working sub- 
stance, cannot be drawn. 

We may, however, use the temperature-entropy diagram 
(like Fig. 30, page 104, or the plate at the end of the book) for 
solving problems connected with that cycle instead of equations 
(143) and (144)- 

In the first place we have by equa- 
tion (96), page S3, 



I 



cdl, 



and by equation (113), page 97, 



-/ 



cdt 
T 



for a volatile liquid. From the latter 
we have 

cdt = TdO; 

therefore 



/ 



= / TdO. 




Fig. 34- 



From this last equation it is evident that the heat of the liquid qi 
for water represented by the point a in Fig. 34, is measured by 



138 THE STEAM-ENGINE 

the area Omao. In like manner the heat of the liquid q^ cor- 
responding to the point d, is represented by the area Omdn. 
Again, the heat added during the vaporization represented by 

ah, is ^j, while the increase of entropy is — ^ . Therefore the heat 

of vaporization can be represented by the area oahp. In like 
manner the partial vaporization x^r^ can be represented by the 
area ndcp. Therefore the heat changed into work for the cycle 
in Fig. 33, which has been represented by 

^1 + ?i - (^2^2 + ?2)> 
can equally well be represented by the area 

abed = area Omao + area oahp 
— (area Omdn + area ndcp). 

It will consequently be sufficient to measure the area abed 
by any means, for example, by aid of a planimeter, in order to 
determine the heat changed into work during the operation of the 
non-conducting engine working on the Rankine cycle. If the plan- 
imeter determines the area in square inches, the scale of the draw- 
ing for Fig. 34 should be one inch per degree, and one inch per 
unit of entropy, or, if other and more convenient scales are to be 
used, proper reductions must be made to allow for those scales. 

It must be firmly fixed in mind that the use of a diagram like 
Fig. 34 is justified because it has been proved that the area 
abed (drawn to the proper scale) is numerically equal to the 
heat changed into work as computed by equation (143), and 
that the diagram does not represent the operations of the cycle. 
This is entirely different from the case of the diagram. Fig. 32, 
which icorrectly represents the operations of Carnot 's cycle. 

The illustration of the use of the temperature-entropy diagram 
for this purpose is chosen for convenience with dry saturated 
steam at b, Fig. 34. It is evident that it could (with equal 
propriety) be applied to an engine supplied with moist steam if 
r^ is replaced by x^r^ in equation (143) and if b is located at the 
proper place between a and b. 

The actual measurement of areas by a planimeter is seldom 



INCOMPLETE CYCLE 1 39 

if ever applied, but the diagram is used effectively in the dis- 
cussion of certain problems of non-reversible flow of steam in 
nozzles and turbines, with allowance for friction. 

It further suggests an approximation that may sometimes be 
useful, especially if the change of pressure (and temperature) is 
small. Thus the area ahcd may be approximately represented 
by the expression 

i (ah + dc) be = \{^ + ^) (.h - h), 

SO that in place of equation (143) we may have 

for the heat changed into work by Rankine's cycle. 

This approximation depends on treating ah as a straight line, 
and this assumption is more correct as the difference of temper- 
ature is less; that is for those cases in which equation (143) 
deals with the difference of quantities of about the same magni- 
tude, and may consequently be affected by a large relative error. 

Temperature-Entropy Table. — The temperature- entropy table 
which has been described on page 106 was computed for solu- 
tion of problems of this nature, more especially in turbine 
design, and enables us to determine the heat changed into work 
directly with sufficient accuracy for engineering work, without 
interpolation ; it also gives the quality x and the specific volume. 

Incomplete Cycle. — The cycle for a non-conducting engine 
may be incomplete because the expansion is not carried far 
enough to reduce the pressure to that 
of the back-pressure line, as is shown 
in Fig. 35. Such an incomplete cycle 
has less efficiency than a complete cycle, 
but in practice the advantage of using 
a smaller cylinder and of reducing fric- 
tion is sufficient compensation for the 
small loss of efficiency due to a moderate drop at the end of 
the stroke, as shown in Fig. 35. 



p 
a 


h 


^' 




e 













V 



Fig. 35- 



I40 THE STEAM-ENGINE 

The discussion of the incomplete cycle is simplified by assum- 
ing that there is no clearance and no compression as is indicated 
by Fig. 35. It will be shown later that the efficiency will be the 
same with a clearance, provided the compression is complete. 

The most ready way of finding the efficiency for this cycle is 
to determine the work of the cycle. Thus the work during 
admission is 

where u^ is the increase of volume due to vaporization of a pound 
of steam, and cr is the specific volume of water. The work during 
expansion is 

^b - E, =j (/?, + q, - x,p, - q,), 

where q^ and p^ are the heat of the liquid and the heat- equivalent 
of the internal work during vaporization at the pressure p^, 
while qc and pc are corresponding quantities for the pressure at c. 
x^ is to be calculated by the equation 



- = ^&^^-'')- 



The work done by the piston on the steam during exhaust is 

The total work of the cycle is obtained by adding the work 
during admission and expansion and subtracting the work 
during exhaust, giving 

J (p^ + Ap^u, - x,p, - Ap.j)c,u, + 9i - q,) + (/>, - p^) 0-. (146) 

The last term is small, and may be neglected. Adding and 
subtracting Ap^x^u^ and multiplying by ^, we get for the heat- 
equivalent of the work of the cycle 

Qi- Q2 = ^1- ^crc + ^(/ - P2) ^'^c +qt- qc (147) 



STEAM-CONSUMPTION OF NON-CONDUCTING ENGINE 141 

which is equal to the difference between the heat suppHed and 
the heat rejected as indicated. The heat supplied is 

61 = ^ + ?i - (Iv 
as was deduced for the complete cycle; the cost of making the 
steam remains the same, whether or not it is used efficiently. 
Finally, the efficiency of the cycle is 

e = gi ~ Q2 _ r, + q, - ^crc - qc + A {p, - p,) x,u, 

<2i ^ + ?i - q, 

^ + ?i - ?2 

If pc is made equal to p\ in the preceding equation, it will be 
reduced to the same form as equation (144), because the expan- 
sion in such case becomes complete. 

Steam-Consumption of Non-conducting Engine. — A horse- 
power is 33000 foot-pounds per minute or 60 X 33000 foot-pounds 
per hour. But the heat changed into work per pound of steam 
by a non-conducting engine with complete expansion is, by 
equation (143), 

''1 + ?1 - ?2 - ^2^V 

SO that the steam required per horse-power per hour is 

60 X 33000 

778 K + ?i - ?2 - ^2^2) 

Similarly, the steam per horse-power per hour for an engine 
with incomplete expansion, by aid of expression (146), is 

60 X 33000 

778 {p^ + Ap^u^ - x,p, - Ap^x.u, + ?i - qc)' 

The value of x^ or Xc is to be calculated by the general equation 

The denominator in either of the above expressions for the 
steam per horse-power per hour is of course the work done per 
pound of steam, and the parenthesis without the mechanical 



(i49) 



142 THE STEAM-ENGINE 

equivalent 778 is equal to Q^ — Q^. If then we multiply and 
divide by 

Qi = ^1 + ?i - ?2. 

that is, by the heat brought from the boiler by one pound of 
steam, we shall have in either case for the steam consumption 
in pounds per hour 

60 X 33000 X Q, 60 X 33000 

where 

is the efficiency for the cycle. 

Actual Steam-Engine. — The indicator-diagram from an actual 
steam-engine differs from the cycle for a non-conducting engine 
in two ways: there are losses of pressure between the boiler and 
the cylinder and between the cylinder and the condenser, due 
to the resistance to the flow of steam through pipes, valves, and 
passages; and there is considerable interference of the metal of 
the cylinder with the action of the steam in the cylinder. The 
losses of pressure may be minimized for a slow-moving engine 
by making the valves and passages direct and large. The 
interference of the walls of the cylinder cannot be prevented, 
but may be ameliorated by using superheated steam or by steam- 
jacketing. 

When steam enters the cylinder of an engine, some of it is 
condensed on the walls which were cooled by contact %with 
exhaust-steam, thereby heating them up nearly to the tempera- 
ture of the steam. After cut-off the pressure of the steam is 
reduced by expansion and some of the water on the walls of 
the cylinder vaporizes. At release the pressure falls rapidly 
to the back-pressure, and the water remaining on the walls is 
nearly if not all vaporized. It is at once evident that so much 
of the heat as remains in the walls until release and is thrown 
out during exhaust is a direct loss; and again, the heat which 
is restored during expansion does work with less efficiency^ 



ACTUAL STEAM-ENGINE 1 43 

because it is reevaporated at less than the temperature in the 
boiler or in the cylinder during admission. A complete state- 
ment of the action of the walls of the cylinder of an engine, 
with quantitative results from tests on engines, was first given 
by Hirn. His analysis of engine tests, showing the interchanges 
of heat between the walls of the cylinder and the steam, will be 
given later. It is sufficient to know now that a failure to con- 
sider the action of the walls of the cylinder leads to gross errors, 
and that an attempt to base the design of an engine on the theory 
of a steam-engine with a non-conducting cylinder can lead only 
to confusion and disappointment. 

The most apparent effect of the influence of the walls of the 
cylinder on the indicator-diagram is to change the expansion 
and the compression lines ; the former exhibits this change most 
clearly. In the first place the fluid in the cylinder at cut-off 
consists of from twenty to fifty per cent hot water, which is found 
mainly adhering to the walls of the cylinder. Even if there 
were no action of the .walls during expansion the curve would be 
much less steep than the adiabatic line for dry saturated steam. 
But the reevaporation during expansion still further changes the 
curve, so that it is usually less steep than the rectangular 
hyperbola. 

It may be mentioned that the fluctuations of temperature 
in the walls of a steam-engine cylinder caused by the conden- 
sation and reevaporation of water do not extend far from the sur- 
face, but that at a very moderate depth the temperature remains 
constant so long as the engine runs under constant conditions. 

The performance of a steam-engine is commonly stated in 
pounds of steam per horse-power per hour. For example, a 
small Corliss engine, developing 16.35 horse-power when 
running at 61.5 revolutions per minute under 77.4 pounds 
boiler-pressure, used 548 pounds of steam in an hour. The 
steam consumption was 

548 -^ 16.35 = 33-5 • 

pounds per horse-power per hour. 



144 



THE STEAM-ENGINE 



This method was considered sufficient in the earlier history 
of the steam-engine, and may now be used for comparing simple 
condensing or non-condensing engines which use saturated 
steam and do not have a steam-jacket, for the total heat of steam, 
and consequently the cost of making steam from water at a given 
temperature increases but slowly with the pressure. 

The performance of steam-engines may be more exactly 
stated in British thermal units per horse-power per minute. 
This method, or some method equivalent to it, is essential in 
making comparisons to discover the advantages of superheat- 
ing, steam-jacketing, and compounding. For example, the 
engine just referred to used steam containing two per cent of 
moisture, so that x^ at the steam-pressure of 77.4 pounds was 
0.98. The barometer showed the pressure of the atmosphere 
to be 14.7 pounds, and this was also the back-pressure during 
exhaust. If it be assumed that the feed-water was or could 
be heated to the corresponding temperature of 212° F., the 
heat required to evaporate it against 77.4 pounds above the 
atmosphere or 92.1 pounds absolute was 

^/i + ?i ~ ?2 ^ o-9^ ^ 888.0 + 292.1 - 180.3 = 982.0 B.T.U. 
The thermal units per horse-power per minute were 

60 

Efficiency of the Actual Engine. — When the thermal units 
per horse-power per minute are known or can be readily cal- 
culated, the efficiency of the actual steam-engine may be found by 
the following method : A horse-power corresponds to the develop- 
ment of 33000 foot-pounds per minute, which are equivalent to 
33000 -^ 778 = 42.42 

thermal units. This quantity is proportional to Q^ — Q^y and 
the thermal units consumed per horse-power per minute are 
proportional to Q^, so that the efficiency is 

g _ QjL^Z^^ 42-42 ^ 

Qj B.T.U. per H.P. per min. * 



EFFICIENCY OF THE ACTUAL ENGINE 



145 



For example, the Corliss engine mentioned above had an 
efficiency of 

42.42 -r 548 - 0.077. 

This same method may evidently be applied to any heat- 
engine for which the consumption in thermal units per horse- 
power per hour can be apphed. 

From the tests reported in Chapter XIII it appears that the 
engine in the laboratory of the Massachusetts Institute of Tech- 
nology on one occasion used 13.73 pounds of steam per horse- 
power per hour, of which 10.86 pounds were supplied to the 
cylinders and 2.87 pounds were condensed in steam-jackets on the 
cylinders. The steam in the supply-pipe had the pressure of 
1.57.7 pounds absolute, and contained 1.2 per cent of moisture. 
The heat supplied to the cylinders per minute in the steam 
admitted was 

10.86 (x/j + q^- q^) - 60 

= 10.86 (0.988 X 858.6 -f 333.9 - 120.0) -V- 60 

= 191 B.T.U. ; 

^2 being the heat of the liquid at the temperature of the back- 
pressure of 4.5 pounds absolute. 

The steam condensed in the steam-jackets was witMrawn 
at the temperature due to the pressure and could have been 
returned to the boiler at that temperature; consequently the 
heat required to vaporize it was r^, and the heat furnished by 
the steam in the jackets was 

2.87 X 0.98 X 858.6 -=- 60 = 40.6 B.T.U. 
The heat consumed by the engine was 

191 -f 40.6 = 232 B.T.U. 

per horse-power per minute, and the efficiency was 
e = 42.42 -^ 232 = 0.183. 



146 THE STEAM-ENGINE 

The efficiency of Carnot 's cycle for the range of temperatures 
corresponding to 157.7 and 4.5 pounds absolute, namely, 82i°.7 
and 61 7°. 2 absolute, is 

T. - r„ 821.7 — 617.2 

e = -^ — 2 == '- '— = 0.248. 

T^ 821.7 

The efficiency for a non-conducting engine with complete 
expansion, calculated by equation (144), is for this case 

X r^ 0.821 X 1004.1 

J — — = 0.227 



^ + ?i - ?2 S58.6 + 333-9 - 126.0 

where x^ is calculated by the equation 

617.2 / 858.6 , „ ■ \ _ 

= — ' — • I -r V 0.^180 - 0.2282 = 0.821. 

1004.1 \821.7 •" ^ I 

During the test in question the terminal pressure at the end of 
the expansion in the low-pressure cylinder was 6 pounds abso- 
lute, which gives 

629.6 /858.6 ,0 \ o 

= ^(d7:7 + °-5'«9-°-475J= 0.832, 

and the efficiency by equation (148) was 
^/// _ J __ ^c^c - Qc + q,. - A (p, - p.^) x,u, 

^1 + ?1 - ?2 
_ _ 0.832X995.8- 138.0+ 126.0+^1(6-4.5)0.832 X62 

858-6 + 333.9 - 126.0 



= 0.222. 



The real criterion of the perfection of the action of an engine 
is the ratio of its actual efficiency to that of a perfect engine. 
If for the perfect engine we choose Carnot 's cycle the ratio is 

e 0.18^ ^ 

-; = ;f- = 0.7^6. 

e' 0.2485 ^^ 



EFFICIENCY OF THE ACTUAL ENGINE 147 

But if we take for our standard an engine with a cylinder of non- 
conducting material the ratio for complete expansion is 

e o.i8s o 

- = f- = 0.807. 

e" 0.227 

For incomplete expansion the ratio is 

e 0.183 o 

— = ^ =0.824. 

e'" 0.222 

To complete the comparison it is interesting to calculate 
the steam-consumption for a non-conducting steam-engine by 
equation (149), both for complete and for incomplete expan- 
sion. For complete expansion we have 

60 X 3SOOO J 
^- =10.5 pounds, 



778 X 0.227 (858.6 + 333.9 - 126.0) 

and for incomplete expansion 

60 X 33000 ■ 

778 X 0.222 (858.6 -f 333.9 - 126.0) 



= 10.7 pounds 



per horse-power per hour. 

But if these steam-consumptions are compared with the 
actual steam-consumption of 13.73 pounds per horse-power 
per hour, the ratios are 

IO-5 -^ 1373 = 0-766 and 10.7 -^ 13.73 = 0.783, 

which are very different from the ratios of the efficiencies. The 
discrepancy is due to the fact that more than a fourth of the 
steam used by the actual engine is condensed in the jackets 
and returned at full steam temperature to the boiler, while the 
non-conducting engine has no jacket, but is assumed to use all 
the steam in the cylinder. 

From this discussion it appears that there is not a wide margin 
for improvement of a well-designed engine running under favor- 
able conditions. Improved economy must be sought either by 
increasing the range of temperatures (raising the steam- pressure 



148 



THE STEAM-ENGINE 



or improving the vacuum), or by choosing some other form of 
heat-motor, such as the gas-engine. 

Attention should be called to the fact that the real criterion of 
the economy of a heat-engine is the cost of producing power by 
that engine. The cost may be expressed in thermal units per 
horse-power per minute, in pounds of steam per horse-power 
per hour, in coal per horse-power per hour, or directly in money. 
The expression in thermal units is the most exact, and the best 
for comparing engines of the same class, such as steam-engines. 
If the same fuel can be used for different engines, such as steam- 
and gas-engines, then the cost in pounds of fuel per horse-power 
per hour may be most instructive. But in any case the money 
cost must be the final criterion. The reason why it is not more 
frequently stated in reports of tests is that it is in many cases 
somewhat difficult to determine, and because it is affected by 
market prices which are subject to change. 

At the present time a pressure as high as 150 pounds above 
the atmosphere is used where good economy is expected. It 
appears from the table on page 132, showing the efficiency of 
Carnot's cycle for various pressures, that the gain in econom}- 
by increasing steam-pressure above 150 pounds is slow. The 
same thing is shown even more clearly by the following table: 

EFFECT OF RAISING STEAM-PRESSURE. 



Boiler- 


Efficiency, 
Carnot's Cycle. 


Non-conducting Engine. 


Probable Performance, 
Actual Engine. 


pressure by 
Gauge. 


Efficiency. 


B.T.U. per 
H.P. per 
Minute. 


B.T.U. per 
H.P. per 
Minute. 


Steam per 

H.P. per 

Hour. 


150 
200 
300 


0.302 
0.320 
0.347 


0.272 
0.288 
0.306 


156 
147 


195 
184 
169 


IO-5 
9.6 



In the calculations for this table the steam is supposed to be 
dry as it enters the cylinder of the engine, and the back-pressure 
is supposed to be 1.5 pounds absolute, while th6 expansion for 
the non-conducting engine is assumed to be complete. The 



CONDENSERS 



149 



heat-consumption of the non-conducting engine is obtained by 
dividing 42.42 by the efficiency; thus for 150 pounds 
42.42 ^ 0.272 = 156. 

The heat-consumption of the actual engine is assumed to be 
one-fourth greater than that of the non-conducting engine. The 
steam-consumption is calculated by the reversal of the method 
of calculating the thermal units per horse-power per minute 
from the steam per horse-power per hour, and for simplicity 
all of the steam is assumed to be supplied to the cylinder. But 
an engine which shall show such an economy for a given pressure 
as that set down in the table must be a triple or a quadruple 
engine and must be thoroughly steam-jacketed. The actual 
steam-consumption is certain to be a little larger than that given 
in the table, as steam condensed in a steam-jacket yields less 
heat than that passed through the cylinder. 

It is very doubtful if the gain in fluid efficiency due to increasing 
steam- pressure above 1 50 or 200 pounds is not offset by the greater 
friction and the difficulty of maintaining the engine. Higher 
pressures than 200 pounds are used only where great power must 
be developed with small weight and space, as in torpedo-boats. 

Condensers. — Two forms of condensers are used to condense 
the steam from a steam-engine, known as jet-condensers and 
surface-condensers. The former are commonly used for land 
engines; they consist of a receptacle having a volume equal to 
one-fourth or one-third of that of the cylinder or cylinders that 
exhaust into it, into which the steam passes from the exhaust-pipe 
and where it meets and is condensed by a spray of cold water. 

If it be assumed that the steam in the exhaust-pipe is dry 
and saturated and that it is condensed from the pressure p and 
cooled to the temperature /^^j then the heat yielded per pound 
of steam is ^ _ ^^^ 

where H is the total heat of steam at the pressure p^ and q^ is the 
heat of the liquid at the temperature t]c. The heat acquired by 
each pound of condensing or injection water is 

qk - Qh 



150 THE STEAM-ENGINE 

where q^ is the heat of the liquid at the temperature /, of the 
injection- water as it enters the condenser. Each pound of steam 
will require 

G = ^.±±^^ (^ ^) 

qic -qi ^ ^ 

pounds of injection-water. 

For example, steam at 4 pounds absolute has for the total 
heat 1 1 28.6. If the injection- water enters with a temperature 
of 60° F., and leaves with a temperature of 120° F., then each 
pound of steam will require 

r + q — q^ _ 11 28.6 — 88.0 _ 

qk - qi ~ 88.0 - 28.12 ~ ^^'^ 

pounds of injection-water. This calculation is used only to 
aid in determining the size of the pipes and passages leading 
water to and from the condenser, and the dimensions of the air- 
pump. Anything like refinement is useless and impossible, 
as conditions are seldom well known and are liable to vary. 
From 20 to 30 times the weight of steam used by the engine is 
commonly taken for this purpose. 

The jet-condensers cannot be used at sea when the boiler- 
pressure exceeds 40 pounds by the gauge; all modern steamers 
are consequently supplied with surface-condensers which consist 
of receptacles, which are commonly rectangular in shape, into 
which steam is exhausted, and where it is condensed on horizontal 
brass tubes through which cold sea-water is circulated. The 
condensed water is drained out through the air-pump and is 
returned to the boiler. Thus the feed-water is kept free from 
salt and other mineral matter that would be pumped into the 
boiler if a jet-condenser were used, and if the feed-water were 
drawn from the mingled water and condensed steam from 
such a condenser. Much trouble is, however, experienced 
from oil used to lubricate the cylinders of the engine, as it is 
likely to be pumped into the boilers with the feed-water, even 
though attempts are made to strain or filter it from the water. 

The water withdrawn from a surface-condenser is likely to 



AIR-PUMP 



151 



have a different temperature from the cooHng water when it 
leaves the condenser. If its temperature is /^ then we have 
instead of equation (150) 

G = '-±^^ (151) 

qk - qi 

for the coohng water per pound of steam. The difference is 
really immaterial, as it makes little difference in the actual value 
of G for any case. 

Cooling Surface. — Experiments on the quantity of cooling 
surface required by a surface-condenser are few and unsatis- 
factory, and a comparison of condensers of marine engines 
shows a wide diversity of practice. Seaton says that with an 
initial temperature of 60°, and with 120° for the feed- water, a 
condensation of 13 pounds of steam per square foot per hour 
is considered fair work. A new condenser in good condition 
may condense much more steam per square foot per hour than 
this, but allowance must be made for fouling and clogging, 
especially for vessels that make long voyages. 

Seaton also gives the following table of square feet of cooling 
surface per indicated horse-power: 

Absolute Terminal Pressure, 
Pounds per Square Inch. 

20 

15 



Squ 
per 


are Feet 
I. H.P. 




•17 




57 




50 




43 




37 




30 



I2i 

10 

8 

6 

For ships stationed in the tropics, allow 20 per cent more; 
for ships which occasionally visit the tropics, allow 10 per cent 
more; for ships constantly in a cold climate, 10 per cent less 
may be allowed. 

Air-Pump. — The vacuum in the condenser is maintained 
by the air-pump, which pumps out the air which finds its way 
there by leakage or otherwise; the condensing water carries 



152 THE STEAM-ENGINE 

a considerable volume of air into the condenser, and the size 
of the air-pump can be based roughly on the average percentage 
of air held in solution in water; the air which finds its way into 
a surface-condenser enters mainly by leakage around the low- 
pressure piston-rod and elsewhere. 

It is customary to base the size of the air-pump on the dis- 
placement of the low-pressure piston (or pistons); for example, 
the capacity of a single-acting vertical air-pump for a merchant 
steamer, with triple- expansion engines, may be about 2V of the 
capacity of the low-pressure cylinder. 

With the introduction of steam-turbines, the importance of 
a good vacuum becomes more marked, and the duty of the air- 
pump, which commonly removes air and also the water of con- 
densation from the condenser, is divided between a dry-air 
pump, which removes air from the condenser, and a water- 
pump, which removes the water of condensation. Air-pumps 
are treated more at length on page 374, in connection with the 
discussion of compressed air. 

Designing Engines. — The only question that is properly 
discussed here is the probable form of the indicator-diagram, 
which gives immediately the method of finding the mean effective 
pressure, and, consequently, the size of the cylinder of the engine. 

The most reliable way of finding the expected mean effective 
pressure in the design of a new engine is to measure an indicator- 
diagram from an engine of the same or similar type and size, 
and working under the same conditions. 

If a new engine varies so 

PBoilerpressnre ^^^^1 ilOm the typC OU which 

the design is based that the 

diagram from the latter cannot 

be used directly, the following 

method may be used to allow 

Fig. 3sa. for modcratc changes of boiler 

pressure or expansion. The 

type diagram either on the original card or redrawn to a larger 

scale, may have added to it the axis of zero pressure and vol- 




DESIGNING ENGINES 1 53 

ume OV and OP (Fig. 35a). The former is laid off parallel to 
the atmospheric line and at a distance to represent the pressure 
of the atmosphere, using the scale for measuring pressure on the 
diagram. The latter is drawn vertical and at a distance from af 
which shall bear the same ratio to the length of the diagram as 
the clearance space of the cylinder has to the piston-displace- 
ment. The boiler-pressure line may be drawn as shown. The 
absolute pressure may now be measured from O V with the proper 
scale and volume from OP with any convenient scale. 

Choosing points a and b at the beginning and end of expan- 
sion determine the exponent for an exponential equation by the 
method on page 66; do the same for the compression curve cf. 

Draw a diagram like Fig. 35 for the new engine, making the 
proper allowance for change of boiler- pressure or point of cut- 
off, using the probable clearance for determining the position 
of the line af. Allowing for loss of pressure from the boiler to 
the cylinder, and for wire-drawing or loss of pressure in the 
valves and passages, locate the points a and b. The back- 
pressure line de can be drawn from an estimate of the probable 
vacuum. The volumes at c and e are determined by the action 
of the valve gear. By aid of the proper exponential equations 
locate a few points on be and ef and sketch in those curves. 
Finish the diagram by hand by comparison with the type dia- 
gram. If necessary draw two such diagrams for the head and 
crank ends of the cylinder. The mean effective pressure can 
now be determined by aid of the planimeter and used in the 
design of the new engine. 

Usually the refinements of the method just detailed are 
avoided, and an allowance is made for them in the lump by a 
practical factor. The following approximations are made: 
(i) the pressure in the cylinder during admission is assumed 
to be the boiler pressure, and during the exhaust the vacuum 
in the condenser; (2) the release is taken to be at the end of 
the stroke; (3) both expansion and compression lines are treated 
as hyperbolae. The mean effective pressure is then readily 
computed as indicated in the following example. 



154 



THE STEAM-ENGINE 



Problem. — Required the dimensions of the cylinder of an 
engine to give 200 horse- power; revolutions 100; gauge pressure 
80 pounds; vacuum 28 inches; cut-off at \ stroke; release at end 
of stroke; compression at jV stroke; clearance 5 per cent. 

The absolute boiler-pressure is 94.7 pounds, and the absolute 
pressure corresponding to 28 inches of mercury is nearly one 
pound. It is convenient to take the piston displacement as 
one cubic foot and the stroke as one foot for the purpose of 
determining the mean effective pressure. The volume of cut- 
off is consequently i cubic foot due to the motion of the piston 
plus To cubic foot due to the clearance or 0.35 cubic foot; the 
volume at release is 1.05 cubic foot, and at compression is 0.15 
cubic foot. 

The work during admission (corresponding to a6, Fig. 35a) is 

94.7 X 144 X 0.35 foot-pound, 
and during expansion is 

p^v^ log,^ = 94.7 X 144 X 0.35 loge ^• 

The work during exhaust done by the piston in expelling the 
steam is 

I X 144 X (i - 0.15)^ 

and the work during compression is 

, CIS 

I X 144 X 0.1 S ioge ^• 

0.05 

The mean effective pressure in pounds per square inch is 
obtained by adding the first two works and subtracting the last 
two and then dividing by 144, so that 

M.E.P. = 94.7 X 0.25 -V 94.7 X 0.35 log, ^. 

0-35 

- I X 0.85 - I X 0.15 loge ^^ = 59.1. 

0.05 

The probable mean effective pressure may be taken as t% 
of this computed pressure, or 53.2 pounds per square inch. 



DESIGNING ENGINES 



155 



Given the diameter and stroke of an engine together with the 
mean effective pressure, and revolutions, we may find the horse- 
power by the formula 

I.H.P. = ^ ^^^^ 
33000 

where j^ is the mean effective pressure, / is the stroke in feet, a is 
the area of the circle for the given diameter in square inches, and 
n is the number of revolutions per minute. For our case we 
may assume that the stroke is twice the diameter, whence 

















?.d 




ird' 










2 


X 


s,s« 


,2 


X 




X 




X 


100 


200 


__ 














12 




^ 







33000 

/. d = 16.8 inches, 5 = 33.6 inches. 

In practice the diameter would probably be made i6| inches 
and the stroke ^^i inches. 



CHAPTER IX. 



COMPOUND ENGINES. 



A COMPOUND engine has commonly two cylinders, one of 
which is three or four times as large as the other. Steam from 
a boiler is admitted to the small cylinder, and after doing work in 
that cylinder it is transferred to the large cylinder, from which 
it is exhausted, after doing work again, into a condenser or 
against the pressure of the atmosphere. If we assume that the 
steam from the small cylinder is exhausted into a large receiver, 
the back-pressure in that cylinder and the pressure during the 
admission to the large cylinder will be uniform. If, further, we 
assume that there is no clearance in either cyHnder, that the 
back-pressure in the small cylinder and the forward pressure in 
the large cylinder are the same, and that the expansion in the 
small cyUnder reduces the pressure down to the back-pressure in 
that cylinder, the diagram for the small cylinder will be A BCD, 




F V 




Fig. 36. 



Fig. 37- 



Fig. 36, and for the large cylinder DCFG. The volume in the 
large cylinder at cut-off is equal to the total volume of the small 
cylinder, since the large cylinder takes from the receiver the same 
weight of steam that is exhausted by the small cylinder, and, in 
this case, at the same pressure. 

The case just discussed is one extreme. The other extreme 
occurs when the small cylinder exhausts directly into the large 

156 



COMPOUND ENGINES 1 57 

cylinder without an intermediate receiver. In such engines the 
pistons must begin and end their strokes together. They may 
both act on the beam of a beam engine, or they may act on one 
crank or on two cranks opposite each other. 

For such an engine, A BCD, Fig. 37, is the diagram for the 
small cylinder. The steam line and expansion line AB and BC 
are like those of a simple engine. When the piston of the small 
cylinder begins the return stroke, communication is opened with 
the large cylinder, and the steam passes from one to the other, 
and expands to the amount of the difference of the volume, it 
being assumed that the communication remains open to the end 
of the stroke. The back-pressure line CD for the small cylinder, 
and the admission line HI for the large cylinder, gradually fall 
on account of this expansion. The diagram for the large cylin- 
der is HIKG, which is turned toward the left for convenience. 

To combine the two diagrams, draw the line abed, parallel to 
V'OV, and from h lay off hd equal to ca; then d is one point of the 
expansion curve of the combined diagram. The point C corre- 
sponds with H, and E, corresponding with /, is as far to the right 
as / is to the left. 

For a non-conducting cylinder, the combined diagram for a 
compound engine, whether with or without a receiver, is the same 
as that for a simple engine which has a cylinder the same size 
as the large cylinder of the compound engine, and which takes 
at each stroke the same volume of steam as the small cylinder, 
and at the same pressure. The only advantage gained by the 
addition of the small cylinder to such an engine is a more even 
distribution of work during the stroke, and a smaller initial stress 
on the crank-pin. 

Compound engines may be divided into two classes — those 
with a receiver and those without a receiver; the latter are called 
" Woolf engines " on the continent of Europe. Engines without 
a receiver must have the pistons begin and end their strokes at 
the same time; they may act on the same crank or on cranks 180° 
apart. The pistons of a receiver- compound engine may make 
strokes in any order. A form of receiver compound engine with 



158 COMPOUND ENGINES 

two cylinders, commonly used in marine work, has the cranks at 
go° to give handiness and certainty of action. Large marine 
engines have been made with one small cylinder and two large 
or low-pressure cylinders, both of which draw steam from the 
receiver and exhaust to the condenser. Such engines usually 
have the cranks at 120°, though other arrangements have been 
made. 

Nearly all compound engines have a receiver, or a space 
between the cylinders corresponding to one, and in no case is 
the receiver of sufficient size to entirely prevent fluctuations of 
pressure. In the later marine work the receiver has been made 
small, and frequently the steam-chests and connecting pipes have 
been allowed to fulfil that function. This contraction of size 
involves greater fluctuations of pressure, but for other reasons it 
appears to be favorable to economy. 

Under proper conditions there is a gain from using a com- 
pound engine instead of a simple engine, which may amount to 
ten per cent or more. This gain is to be attributed to the division 
of the change of temperature from that of the steam at admission 
to that of exhaust into two stages, so that there is less fluctua- 
tion of temperature in a cylinder and consequently less inter- 
change of heat between the steam and the walls of the cylinder. 
Compound Engine without Receiver. — The indicator-dia- 
grams from a compound engine without a receiver are repre- 
sented by Fig. 38. The steam line and expan- 
sion line of the small cylinder, AB and BC, do 
not differ from those of a simple engine. At C 
the exhaust opens, and the steam suddenly 
expands into the space between the cylinders 
and the clearance of the large cylinder, and the 
pressure falls from C to D. During the return 
stroke the volume in the large cylinder increases more rapidly 
than that of the small cylinder decreases, so that the back-press- 
ure line DE gradually falls, as docs also the admission line HI 
of the large cylinder, the difference between these two lines being 
due to the resistance to the flow of steam from one to the other. 




COMPOUND ENGINE WITH RECEIVER 



159 



At E the communication between the two cylinders is closed by 
the cut-off of the large cylinder; the steam is then compressed 
in the small cylinder and the space between the two cylinders 
to F, at which the exhaust of the small cylinder closes; and the 
remainder of the diagram FGA is like that of a simple engine. 
From 7, the point of cut-off of the large cylinder, the remainder 
of the diagram IKLMNH is like the same part of the diagram 
of a simple engine. 

The difference between the lines ED and HI and the '' drop " 
CD at the end of the stroke of the small piston indicate waste 
or losses of efficiency. The compression EFG and the accom- 
panying independent expansion IK in the large cylinder show a 
loss of power when compared with a diagram like Fig. 37 for an 
engine which has no clearance or intermediate space; but com- 
pression is required to fill waste spaces with steam. The com- 
pression EF is required to reduce the drop CZ>, and the compres- 
sion FG fills the clearance in anticipation of the next supply from 
the boiler. Neither compression 
is complete in Fig. 2^^. 

Diagrams from a pumping en- 
gine at Lawrence, Massachusetts, 
are shown by Fig. 39. The 
rounding of corners due to the 
indicator makes it difficult to de- 
termine the location of points like 
D, E, F, and / on Fig. 38. The 
low-pressure diagram is taken 
with a weak spring, and so has an 
exaggerated height. 

Compound Engine with Receiver. — It has already been 
pointed out that some receiver space is required if the cranks 
of a compound engine are to be placed at right angles. When 
the receiver space is small, as on most marine engines, the fluc- 
tuations of pressure in the receiver are very notable. This is 
exhibited by the diagrams in Fig. 40, which were taken from a 
yacht engine. An intelligent conception of the causes and meaning 





Fig. 39. 




l6o COMPOUND ENGINES 

of such fluctuations can be best obtained by constructing ideal 
diagrams for special cases, as explained on page 164. 

Triple and Quadruple Expansion - 
Engines. — The same influences which 
introduced the compound engines, when 
the common steam-pressure changed 
from forty to eighty pounds to the 
square inch, have brought in the succes- 
sive expansion through three cylinders 
^'°" '*°" (the high-pressure, intermediate, and 

low-pressure cylinders) now that 150 to 200 pounds pressure are 
employed. Just as three or more cylinders are combined in 
various ways for compound engines, so four, five, or six cylinders 
have been arranged in various manners for triple-expansion 
engines; the customary arrangement has three cylinders with the 
cranks at 180°. 

Quadruple engines with four successive expansions have been 
employed with high-pressure steam, but with the advisable 
pressures for present use the extra complication and friction 
make it a doubtful expedient. 

Total Expansion. — In Figs. 36 and 37, representing the dia- 
grams for compound engines without clearance and without 
drop between the cylinders, the total expansion is the ratio of 
the volumes at E and at B ; that is, of the low-pressure piston dis- 
placement to the displacement developed by the high-pressure 
piston at cut-off. The same ratio is called the total or equiva- 
lent expansion for any compound engine, though it may have 
both clearance and drop. Such a conventional total expansion 
is commonly given for compound and multiple-expansion engines, 
and is a convenience because it is roughly equal to the ratio of 
the initial and terminal pressures; that is, of the pressure at 
cut-off in the high-pressure cyHnder and at release in the low- 
pressure cylinder. It has no real significance, and is not equiva- 
lent to the expansion in the cylinder of a simple engine, by which 
we mean the ratio of the volume at release to that at cut-off, tak- 
ing account of clearance. And further, since the clearance of 



LOW-PRESSURE CUT-OFF l6i 

the high- and the low-pressure cylinders are different there can 
be no real equivalent expansion. 

If the ratio of the cylinders is R and the cut-off of the high- 
pressure cylinder is at - of the stroke, then the total expansion 
is represented by 

E =^ eR 

^^^ - = R -^ E 



This last equation is useful in determining approximately the 
cut-off of the high-pressure cylinder. 

For example, if the initial pressure is loo pounds absolute and 
the terminal pressure is to be lo pounds absolute, then the total 
expansions will be about lo. If the ratio of the cylinders is 
3I, then the high-pressure cut-off will be about 

- = 3I ^ 10 = 0.35 
of the stroke. 

Low-pressure Cut-off. — The cut-off of the low-pressure 
cylinders in Figs. 36 and 37 is controlled by the ratio of the 
cylinders, since the volumes in the low-pressure cylinder at cut- 
olBf is in each case made equal to the high-pressure piston dis- 
placement; this is done to avoid a drop. If the cut-off were 
lengthened there would be a loss of pressure or drop at the end 
of the stroke of the high-pressure 
piston, as is shown by Fig. 41, 
for an engine with a large receiver 
and no clearance. Such a drop will 
have some effect on the character of 
the expansion line C"F of the low- 
pressure cylinder, both for a non-con- 
ducting and for the actual engine 
with or without a clearance. Its 
principal effect will, however, be on '^* *'* 

the distribution of work between the cylinders; for it is evident 
that if the cut-off of the low-pressure cylinder is shortened the 




l62 COMPOUND ENGINES 

pressure at C" will be increased because the same weight of steam 
is taken in a smaller volume. The back-pressure DO of the 
high-pressure cylinder will be raised and the work will be 
diminished; while the forward pressure DC'^ of the low- 
pressure cylinder will be raised, increasing the work in that 
cylinder. 

Ratio of Cylinders. — In designing compound engines, more 
especially for marine work, it is deemed important for the smooth 
action of the engine that the total work shall be evenly distributed 
upon the several cranks of the engines, and that the maximum 
pressure on each of the cranks shall be the same, and shall not 
be excessive. In case two or more pistons act on one crank, 
the total work and the resultant pressure on those pistons are 
to be considered; but more commonly each piston acts on a 
separate crank, and then the work and pressure on the several 
pistons are to be considered. 

In practice both the ratio of the cylinders and the total expan- 
sions are assumed, and then the distribution of work and the 
maximum loads on the crank-pins are calculated, allowing for 
clearance and compression. Designers of engines usually have 
a sufficient number of good examples at hand to enable them 
to assume these data. In default of such data it may be neces- 
sary to assume proportions, to make preliminary calculations, 
and to revise the proportions till satisfactory results are obtained. 
For compound engines using 80 pounds steam-pressure the ratio 
is 1 : 3 or 1 : 4. For triple-expansion engines the cylinders may 
be made to increase in the ratio i : 2 or i : 2^. 

Approximate Indicator- Diagrams. — The indicator-diagrams 
from some compound and multiple-expansion engines are irreg- 
ular and apparently erratic, depending on the sequence of the 
cranks, the action of the valves, and the relative volumes of the 
cylinders and the receiver spaces. A good idea of the effects and 
relations of these several influences can be obtained by making 
approximate calculations of pressures at the proper parts of the 
diagrams by a method which will now be illustrated. 

For such a calculation it will be assumed that all expansion 



DIRECT-EXPANSION ENGINE 163 

lines are rectangular hyperbolae, and in general that any change 
of volume will cause the pressure to change inversely as the 
volume, further, it will be assumed that when communication 
is opened between two volumes where the pressures are different, 
the resultant pressure may be calculated by adding together the 
products of each volume by its pressure, and dividing by the sum 
of the volumes. Thus if the pressure in a cylinder having the 
volume z'c is pc, and if the pressure is pr in a receiver where 
the volume is Vr, then after the valve opens communication from 
the cylinder to the receiver the pressure will be 

p,V, + pr'Vy 
P = . 

The same method will be used when three volumes are put into 
communication. 

It will be assumed that there are no losses of pressure due to 
throttling or wire-drawing; thus the steam line for the high- 
pressure cylinder will be drawn at the full boiler-pressure, and 
the back-pressure line in the low-pressure cylinder will be drawn 
to correspond with the vacuum in the condenser. iVgain, cylin- 
ders and receiver spaces in communication will be assumed to 
have the same pressure. 

For sake of simplicity the motions of pistons will be assumed 
to be harmonic. 

Diagrams constructed in this way will never be realized in 
any engine; the degree of discrepancy will depend on the type 
of engine and the speed of rotation. For slow-speed pumping- 
engines the discrepancy is small and all irregularities are easily 
accounted for. On the other hand the discrepancies are large 
for high-speed marine-engines, and for compound locomotives 
they almost prevent the recognition of the events of the stroke. . 

Direct- expansion Engine. — If the two pistons of a compound 
engine move together or in opposite directions the diagrams 
are like those shown by Fig. 42. Steam is admitted to the high- 
pressure cylinder from a to b; cut-off occurs at b, and be repre- 
sents expansion to the end of the stroke; be being a rectangular 



164 



COMPOUND ENGINES 



hyperbola referred to the axes O V and OP, from which a, b, and 
c are laid off to represent absolute pressures and volumes, includ- 
ing clearance. 




p p 



Fig. 42. 



At the end of the stroke release from the high-pressure 
cylinder and admission to the low-pressure cylinder are assumed 
to take place, so that communication is opened from the. high- 
pressure cylinder through the receiver space into the low-press- 
ure cylinder. As a consequence the pressure falls from c to d, 
and rises from n to h in the low-pressure cylinder. The line 
O^P^ is drawn at a distance from OP, which corresponds to the 
volume of the receiver space, and the low-pressure diagram is 
referred to O^P^ and O^V as axes. 

The communication between the cylinders is maintained until 
cut-off occurs at i for the low-pressure cylinder. The lines de 
and hi represent the transfer of steam from the high-pressure 
to the low-pressure cylinder, together with the expansion due to 
the increased size of the large cylinder. After the cut-off at i, 
the large cylinder is shut off from the receiver, and the steam in 
it expands to the end of the stroke. The back-pressure and 
compression lines for that cylinder are not affected by compound- 
ing, and are like those of a simple engine. Meanwhile the small 
piston compresses steam into the receiver, as represented by 
ef, till compression occurs, after which compression into the 
clearance space is represented hy fg. The expansion and com- 
pression lines ik and mn are drawn as hyperbolae referred to the 
axes O'P' and O' V\ The compression line ef is drawn as an hyper- 
bola referred to O' V and O^P^j while fg is referred to OF and OP. 



direct-exTpansion engine 165 

In Fig. 42 the two diagrams are drawn with the same scale 
for volume and pressure, and are placed so as to show to the 
eye the relations of the diagrams to each other. Diagrams 
taken from such an engine resemble those of Fig. 39, which 
have the same length, and different vertical scales depending 
on the springs used in the indicators. 

Some engines have only one valve to give release and com- 
pression for the high-pressure cylinder and admission and cut- 
off for the low-pressure cylinder. In such case there is no 
receiver space, and the points e and /coincide. 

When the receiver is closed by the compression of the high- 
pressure cylinder it is filled with steam with the pressure repre- 
sented by /. It is assumed that the pressure in the receiver 
remains unchanged till the receiver is opened at the end of the 
stroke. It is evident that the drop cd may be reduced by short- 
ening the cut-off of the low-pressure cylinder so as to give more 
compression from e io f and consequently a higher pressure at 
/ when the receiver is closed. 

Representing the pressure and volume at the several points 
by p and v with appropriate subscript letters, and represent- 
ing the volume of the receiver by v^, we have the following 
equations : 

pa =" pb = initial pressure; 
Pi = P>n^ back- pressure; 
pc = Pb-Vb -^ 'Vc', 

Pn = Pm'^m ^ '^n', ^ 

Pd = Ph= {pc'Vc + Pn'Vn + PfVr) "^ K + ^^» + ^r); 

Pe = pi = pd (Vc +'Un + "Vr) ^ (^e + '^i + Vr)\ 

Pf = Pe i'Ve + Vr) - (^^ + '^r)', 

Po = Pf^f ^ '^o'y 

Pk = Pi-Vi ^ Vk. 

The pressures p,. and pn can be calculated directly. Then the 
equations for p,i, p^, and p/ form a set of three simultaneous 
equations with three unknown quantities, which can be easily 
solved. Finally, p,j and pjt may be calculated directly. 



l66 COMPOUND ENGINES 

For example, let us find the approximate diagram for a direct- 
expansion engine which has the low-pressure piston displacement 
equal to three times the high-pressure piston displacement. 
Assume that the receiver space is half the smaller piston dis- 
placement, and that the clearance for each cylinder is one-tenth 
of the corresponding piston displacement. Let the cut-off for 
each cylinder be at half-stroke, and the compression at nine- 
tenths of the stroke; let the admission and release be at the end 
of the stroke. Let the initial pressure be 65.3 pounds by the 
gauge or 80 pounds absolute, and let the back-pressure be two 
pounds absolute. 

If the volume of the high- pressure piston displacement be 
taken as unity, then the several required volumes are: 

'Vh = 'Vn = 3 X o-i = 0-3 
,1 Vi = 3 (0.5 +0.1) = 1.8 

'Vk = ^^ = 3 (i-o +0.1) = T,.2> 
V,, = 3 (o.i +0.1) = 0.6 

^r = 0.5 

The pressures may be calculated as follows: 

pa = Pb = ^o; pi = p^ = 2; 

pc = Pb'^b ^ i^c = 80 X 0.6 -^ I.I = 43.6; 

Pn = Pm'i^m - ^„ == 2 X 0.6 ^ O.3 = 4; 

Pe = Pd {'Vc +'Vn + 'Vr) "^ {'^e + ^i + ^^r) = pd (l-I + O.3 + O.5) 

-- (0.6 + 1.8 -f 0.5) = 0.655 pd] 

Pf = pe K + -i^r) - iyf + ^,) = Pe (0.6 + O.5) ^ (o.2 -f O.5) 

= 1.57 p, = 1.57 X 0.655 pd = 1.03 Pd\ 

pd = (Me + Pn-l^n + Pfl^r) ^ iyc + ^„ + ^r) 

= (80 X 0.6 + 4 X 0.3 + 0.5 pf) -^ (0.6 + 0.3 -f 0.5) 

= 25.89 + 0.26 pf] 

pa = 25.89 + 0.26 X 1.03 pa; pd = 35-36; 
p, = Pi = 0.655 pd = 0.655 X 35.36 = 23.2; 
pf = 1-03 P<i = 1.03 X 35.36 = 36.5; 
Pd = PPf - *^p = 36.5 X 0.2 - 0.1 = 73; 
Pk = M- ^ 'Vk = 23.2 X 1.8 -^ 3.3 = 12.6. 



Vb 


= 


0-5 


4- 


0.1 


= 


■ 0.6 


•Vc 


= 


-Va -- 


= ] 


.0 


+ 


0.1 = 


-Ve 


= 


0-5 


+ 


0.1 


= 


0.6 


^/ 


= 


0.1 


+ 


0.1 


= 


0.2 


Va 


= 


0.1 











DIRECT-EXPANSION ENGINE 167 

As the pressures and volumes are now known the diagrams 
of Fig. 42 may be drawn to scale. Or, if preferred, diagrams 
like Fig. 39 may be drawn, making them of the same length and 
using convenient vertical scales of pressure. If the engine runs 
slowly and has abundant valves and passages the diagrams 
thus obtained will be very nearly like those taken from the engine 
by indicators. If losses of pressure in valves and passages are 
allowed for, a closer approximation can be made. 

The mean effective pressures of the diagrams may be readily 
obtained by the aid of a planimeter, and may be used for esti- 
mating the power of the engine. For this purpose we should 
either use the modified diagrams allowing for losses of pressure, 
or we should affect the mean effective pressures by a multiplier 
obtained by comparison of the approximate with the actual dia- 
grams from engines of the same type. For a slow-speed pump- 
ing-engine the multiplier may be as large as 0.9 or even more; 
for high-speed engines it may be as small as 0.6. 

The mean effective pressures of the diagrams may be calcu- 
lated from the volumes and pressures if desired, assuming, of 
course, that the several expansion and compression curves are 
hyperbolae. The process can be best explained by applying it 
to the example already considered. Begin by finding the mean 
pressure during the transfer of steam from the high-pressure 
cylinder to the low-pressure cylinder as represented by de and hi. 
The net effective work during the transfer is 



/ 



pdv = p^ v^ log, ^ = 144 pa {Va +Vn -\- Vr) log /' ^^" ^^ 

'V^ Va + Vh + '^r 

/ . . \ 1 0.6 4- 1.8 -f 0.5 
= 144 X 35.4(1.1 +0.3 -}-o.5)loge ; ; 

I.I +0.3 + 0.5 

= 4120 foot-pounds 

for each cubic foot of displacement of the high-pressure piston. 
This corresponds with our previous assumption of unity for the 
displacement of that piston. The increase of volume is 

v^-i-Vi-^v^ - (va+Vf,+Vr) =o.6-f-i.8-fo.5- (i.i +0.3 -fo.5) = i; 



l68 COMPOUND ENGINES 

SO that the mean pressure during the transfer is 
4120 -^ I X 144 = 28.6 = pjc 

pounds per square inch, which acts on both the high- and the 
low-pressure pistons. 

The effective work for the small cylinder is obtained by add- 
ing the works under ah and he and subtracting the works under 
de, ef, and fg. So that 



Wu 



144 \pa (V — Va) + pbVb loge ~ - px (v d - Vc) 

- pe {Ve + Vr) loge J' , '''' - pfVf loge J7 

= 144 j8o (0.6 - o.i) + 80 X 0.6 loge ^- 28.6 (i.i - 0.6) 
r ^ , N , 0-6 -1- o.:; , , 0.2 ) 

- 23.2 (0.6 + 0.5) loge o^^^fT^ - 36.5 X 0.2 logo — j 

= 144 X 33.26 = 4789 foot-pounds. 

This is the work for each cubic foot of the high- pressure piston 
displacement, and the mean effective pressure on the small piston 
is evidently 33.26 pounds per square inch. 

In a like manner the work of the large piston is 

WL =144 \px iVi — Vh) + pi Vi loge — — pi (Vi —Vn^) — pmVn log» " " [ 

= 144 28.6(1.8-0.3)+ 23.2 X 1.8 log. ^ 

— 2 {^.T, — 0.6) — 2 X 0.6 loge ~^— I = 144 X 61.92 = 8916 foot-pounds. 

Since the ratio of the piston displacements is 3, the work for 
each cubic foot of the low-pressure piston displacement is one-third 
of the work just calculated; and the mean effective pressure on 
the large piston is 

61.92 -^- 3 = 20.64 

pounds per square inch. 

The proportions given in the example lead to a very uneven 
distribution of work; that of the large cylinder being nearly 
twice as much as is developed in the small cylinder. The dis- 



CROSS-COMPOUND ENGINE 



169 



tribution can be improved by lengthening the cut-off of the 
large cylinder, or by changing the proportions of the engine. 

As has already been pointed out, the works just calculated 
and the corresponding mean effective pressures are in excess 
of those that will be actually developed, and must be affected 
by multipliers which may vary from 0.6 to 0.9, depending on 
the type and speed of the engine. 

Cross- compound Engine. — A two-cylinder compound engine 
with pistons connected to cranks at right angles with each other 
is frequently called a cross-compound engine. Unless a large 
receiver is placed between the cylinders the pressure in the space 
between the cylinders will vary widely. 

Two cases arise in the discussion of this engine according as 





6 a 


P 


p' 










A 


















<-Vr-> 












d 




k 


I 


n 





- p 


V !! j 1 : 





n> Ls 


1 

1— : 




1 
1 


q V' 



Fig. 43. 



the cut-off of the large cylinder is earlier or later than half-stroke; 
in the latter case there is a species of double admission to the 
low-pressure cylinder, as is shown in Fig. 43. For sake of 
simplicity the release, and also the admission for each cylinder, 
is assumed to be at the end of the stroke. If the release is early 
the double admission occurs before half-stroke. 

The admission and expansion of steam for the high-pressure 
cylinder are represented by ab and he. At c release occurs, 
putting the small cylinder in communication with the inter- 
mediate receiver, which is then open to the large cylinder. There 
is a drop at cd and a corresponding rise of pressure mn on the 
large piston, which is then at half-stroke; it will be assumed 
that the pressures at d and at n are identical. From d io e the 



170 COMPOUND ENGINES 

Steam is transferred from the small to the large cylinder, and 
the pressure falls because the volume increases; no is the corre- 
sponding line on the low-pressure diagram. The cut-off at 
for the large cylinder interrupts this transfer, and steam is then 
compressed by the small piston into the intermediate receiver 
with a rise of pressure as represented by ef. The admission to 
the large cylinder, tk, occurs when the small piston is at the 
middle of its stroke, and causes a drop, /^, in the small cylinder. 
From g to h steam is transferred through the receiver from the 
small to the large cylinder. The pressure rises at first because 
the small piston moves rapidly while the large one moves slowly 
until its crank gets away from the dead-point; afterwards the 
pressure falls. The line kl represents this action on the low- 
pressure diagram. At h compression occurs for the small 
cylinder, and hi shows the rise of pressure due to compression. 
For the large cylinder the line Im re-presents the supply of steam 
from the receiver, with falling pressure which lasts till the double 
admission at mn occurs. 

The expansion, release, exhaust, and compression in the large 
cylinder are not affected by compounding. 

Strictly, the two parts of the diagram for the low-pressure 
cylinder, mnopq and stklm, belong to opposite ends of the cylin- 
der, one belonging to the head end and one to the crank end. 
With harmonic motion the diagrams from the two ends are 
identical, and no confusion need arise from our neglect to deter- 
mine which end of the large cylinder we are dealing with at any 
time. Such an analysis for the two ends of the cylinder, taking 
account of the irregularity due to the action of the connecting- 
rod, would lead to a complexity that would be unprofitable. 

A ready way of finding corresponding positions of two pistons 
connected to cranks at right angles with each other is by aid 
of the diagram of Fig. 44. Let O be the centre of the crank- 
shaft and pRyRxq be the path of the crank-pin. When one piston 
has the displacement py and its crank is at ORy, the other crank 
may be 90° ahead at OR^ and the corresponding piston displace- 
ment will be px. The same construction may be used if the 



Cl^OSS-COMPOUND ENGINE 



171 




crank is 90° behind or if the angle RyORj; is other than a right 
angle. The actual piston position and crank angles when 
affected by the irregularity due to the 
connecting-rod will differ from those found 
by this method, but the positions found 
by such a diagram will represent the aver- 
age positions very nearly. 

The several pressures may be found as 

follows : Fig. 44. 

pb = pa = initial pressure; 
ps = pq = back-pressure; 

Pc = Pb'Vb -^ '^cl 
Pt = Ps'^s -^ ^o 

Pd = Pn= IPc'Vc + pmi'Vm + ^r) \ -^ {v, -{- V„ + Vr)\ 
Pe = Po = Pd ('Uc + Vn^ + V,.) -^ (v, + V, + Vr)', 
P/= Pe i'Ve +^r) - (^> + Vr) ', 
Pg = Pk = \Pf (Vf + 'Vr) + MS - (1^/+ V, + V,); 

Ph = pi = pg (^/ +Vt ^ V,.) - {vn + vj + ^',.); 

Pm= Pl {I'l + 1'r) ^ i^n + "Vr) ', 

pi = phVh ^ "Vt; 
pp = Mo -^ *^7.- 

The pressures pc and pn can be found directly from the initial 
pressure and the back-pressure, and finally the last two equa- 
tions give direct calculations for pi and pp so soon as pn and po 
are found. There remain six equations containing six unknown 
quantities, which can be readily solved after numerical values 
are assigned to the known pressures and to all the volumes. 

The expansion and compression lines, be and hi, for the high- 
pressure diagrams are hyperbolae referred to the axes OF and 
OP; and in like manner the expansion and compression lines op 
and si, for the low-pressure diagram, are hyperbolae referred to 
O' F' and 0'P\ The curve efis an hyperbola referred to O' F and 
O'P^, and the curve Im is an hyperbola referred to OV^ and 
OP. The transfer lines de and no, gh and kl, are not hyper- 
bolae. They may be plotted point by point by finding corre- 



172 COMPOUND ENGINES 

spending intermediate piston positions, p^^ ^-nd py, by aid of Fig. 
44, and then calculating the pressure for these positions by the 
equation 

PT= Py - Pd {Vd + 'Vm + -^r) -4- {V^ -\-Vy + V^). 

The work and mean effective pressure may be calculated in a 
manner similar to that given for the direct-expansion engine; 
but the calculation is tedious,' and involves two transfers, de and 
nOj and gh and kl. The first involves only an expansion, and 
presents no special difficulty; the second consists of a compres- 
sion and an expansion, which can be dealt with most conveniently 
by a graphical construction. All things considered, it is better 
to plot the diagrams to scale and determine the areas and mean 
effective pressures by aid of a planimeter. 

If the cut-off of the low-pressure is earlier than half-stroke so 
as to precede the release of the high-pressure cylinder the transfer 
represented by de and no, Fig. 43, does not occur. Instead there 
is a compression from d to /and an expansion from / to m. The 
number of unknown quantities and the number of equations are 
reduced. On the other hand, a release before the end of the 
stroke of the high- pressure piston requires an additional unknown 
quantity and one more equation. 

Triple Engines. — The diagrams from triple and other mul- 
tiple-expansion engines are likely to show much irregularity, the 
form depending on the number and arrange- 
ment of the cylinders and the sequence of the 
cranks. A common arrangement for a triple 
engine is to have three pistons acting on 
cranks set equidistant around the circle, as 
shown by Fig. 45. Two cases arise depending 
on the sequence of the cranks, which may be 
in the order, from one end of the engine, of 
high-pressure, low-pressure, and intermediate, as shown by Fig. 
45; or in the order of high-pressure, intermediate, and low- 
pressure. 

With the cranks in the order, high-pressure, low-pressure, and 




TRIPLE ENGINES 



173 



intermediate, as shown by Fig. 45, the diagrams are Hke those 
given by Fig. 46. The admission and expansion for the high- 
pressure cyKnder are represented by ahc. When the high- 
pressure piston is at release, its crank is at H, Fig. 45, and the 
intermediate crank is at /, so that the intermediate piston is 
near half-stroke. If the cut-off for that cylinder is later than 



i \ Scale 160 \ 




1 1 Atmospheric line ^ | 









Fig. 46. 



half-Stroke, it is in communication with the first receiver when 
its crank is at /, and steam may pass through the first receiver 
from the high-pressure to the intermediate cylinder, and there is 
a drop cd, and a corresponding rise of pressure no in the inter- 
mediate cyHnder. The transfer continues till cut-off for the 



174 COMPOUND ENGINES 

intermediate cylinder occurs at p, corresponding to the piston 
position e for the high-pressure cylinder. From the position e 
the high- pressure piston moves to the end of the stroke at /, 
causing an expansion, and then starts to return, causing the 
compression fg. When the high-pressure piston is at g the 
intermediate cylinder takes steam at the other end, causing the 
drop gh and the rise of pressure xl. Then follows a transfer of 
steam from the high-pressure to the intermediate cylinder repre- 
sented by hi and Im. At i the high-pressure compression ik 
begins, and is carried so far as to produce a loop at k. After 
compression for the high-pressure cylinder shuts it from the 
lirst receiver, the steam in that receiver and in the intermediate 
cylinder expands as shown by mn. The expansion in the inter- 
mediate cylinder is represented by pq and the release by qr, 
corresponding to a rise of pressure a/? in the low-pressure cylin- 
der, rs and /?7 represent a transfer of steam from the inter- 
mediate cylinder to the low-pressure cylinder. The remainder 
of the back-pressure line of the intermediate cylinder and the 
upper part of the low-pressure diagram for the low-pressure 
cylinder correspond to the same parts of the high-pressure and 
the intermediate cylinders, so that a statement of the actions in 
detail does not appear necessary. 

The equations for calculating the pressure are numerous, but 
they are not difficult to state, and the solution for a given exam- 
ple presents no special difficulty. Thus we have 



II. 



pa 


= Pb = 


initial pressure; 


Vp = vol. 


first receiver; 


pc 


= pbVb 


^Vc ; 




Vj2= vol. 


second 


receiver; 


Pa 


- po=^ 


[PcVc+P 


n {Vo+Vp)\ - 


4- (Va+Vo +Vr); 






Pe 


= Pp = 


pd (Vd + V 


'o+'yp) ^ {v. 


+ Vp -i- Vp); 






Pf 


= Pe (V 


•e+Vp) -. 


- {vf+ Vp); 








Pa 


= pf{Vf+ Vp) -^ 


iva+ Vp); 








P'^ 


= pl = 


\py{Vg+Vp) + P^V^l 


-^ (vn+vi + Vp); 






pi 


= Pn.= 


ph {Vh + 


Vi + Vp) ^ {Vi +Vm+ Vp); 






p. 


= piVi ■ 


■4- Vk ; 










Pn 


= pm {Vm, + Vp) - 


^ {vn + Vp); 


• 






A 


= Pp'^l 


^-v^', 











TRIPLE ENGINES 175 



pe= py = pr (Vr + Va V^) H- (v^ + Vy-\- Vj^); 
pi = p,iv, + Vji) -f- (Vt+ Vf,); 
P* = Pt {Vt + Vr) ^ {Vu + Vj^y, 

IV. pp= {pu (x;u + Vj^) + priVri\ -^ (v„ + Vri + V^); 

pw= pv (v, + vr, + Vj^) -7- (v„ + V, + v^); 



pm= pwV„ ^ Vx; 

P» = {V, + Vj^) H- {Va + Vj^Yy 

ps = pyVy -T- vs; 

pe = p^ = back-pressure; 

Pv = Pcv^~^ '^'J- 

The pressures at c and at v can be calculated immediately 
from the initial pressure and from the back-pressure. Then it 
will be recognized that there are four individual equations for 
finding pf, p^, pt, and p^. The fourteen remaining equations, 
solved as simultaneous equations, give the corresponding four- 
teen required pressures, some of v^hich are used in calculating 
the four pressures which are determined by the four individual 
equations. The most ready solution may be made by contin- 
uous substitution in the four equations which are numbered at the 
left hand. Thus for pg in equation II, we may substitute, 

p = y, ^/ + ^p _ p ^^ +^P "^z + ^P,_ p 'Vd^rJloj^_y^'iie±v^ ^ 

^ ^Vg +VR 'Vf -\-v^ Vg ^Vp '^v^ + Vp + Vp Vg +Vp 



In the actual computation the several volumes and the proper 
sums of volumes are to be first determined; consequently the 
factors following pa will be numerical factors which may be con- 
veniently reduced to the lowest terms before introduction in the 
equation. This system of substitution will give almost immedi- 
ately four equations with four unknown quantities which may 
readily be solved; after which the determination of individual 
pressures will be easy. In handhng these equations the letters 
representing smaller pressures should be eliminated first, thus 
giving values of higher pressure like pa to tenths of a pound; 
afterward the lower pressure can be determined to a like degree 



176 COMPOUND ENGINES 

of accuracy. A skilled computer may make a complete solu- 
tion of such a problem in two or three hours, which is not exces- 
sive for an engineering method. 

If the cut-off for the intermediate cyhnder occurs before the 
release of the high- pressure cylinder, then the transfer represented 
by de and op does not occur. In like manner, if the cut-off for 
the low-pressure cylinder occurs before the release for the inter- 
mediate cylinder, the transfer represented by rs and /?7 does 
not occur. The omission of a transfer of course simplifies the 
work of deducing and of solving equations. 

In much the same way, equations may be deduced for cal- 
culating pressures when the cranks have the sequence high- 
pressure, intermediate, and low-pressure. The diagrams take 
forms which are distinctly unlike those for the other sequence of 
cranks. In general, the case solved, i.e., high-pressure, low- 
pressure, and intermediate, gives a smoother action for the 
engine. 

For example, the engines of the U. S. S. Machias have the 
following dimensions and proportions: 

High- Inter- Low- 

pressure, mediate, pressure. 

Diameter of piston, inches 15! 22^ 35 

Piston displacement, cubic feet 2.71 5.53 13 -39 

Clearance, per cent 13 14 7 

Cut-off, per cent stroke 66 66 66 

Release, per cent stroke 93 93 93 

Compression, per cent stroke 18 18 18 

Ratio of piston displacements i 2.04 4.94 

Volume first receiver, cubic feet 2.22 

Volume second receiver, cubic feet 6.26 

Ratio of receiver volumes to high-pressure piston dis- 
placement 0.82 2.31 

Stroke, inches 24 

Boiler-pressure, absolute, pounds per sq. in 180 

Pressure in condenser, pounds per sq. in 2 



If the volume of the high-pressure piston displacement is 
taken to be unity, then the volumes required in the equations for 



TRIPLE ENGINES 



177 






Fig- 47. 



calculating pressures, when the cranks have the order high- 
pressure, low-pressure, and intermediate, are as follows: 



V, = 0.79 


v^ ^v^ = 0.29 


Vy=-V^ = 0.35 


^'c = 'Z-'d = 1.06 


v^ = 0.98 


^'^ = 2.02 


Vg = 1. 10 


Vn = Vo = 1-26 


Va = Vp = 2.72 


ly = 1. 13 


^P = 1-63 


T^y = 3.60 


Vg -= Vh = 0.88 


v,^ = V, = 2.18 


vs = V, = 4.94 


z\ = 0.31 


z', = 2.28 


^f = 1.23 


■^^V = I'a = 0.13 


^-'/ = 2.33 

v^ = v^= 1.85 
t;«, = 0.63 





I 78 COMPOUND ENGINES 

The required pressures are: 

Pa = Pb= 150 Pk = 165 Pw = Pz = 25.6 

Pc = 112 pn = 60.0 ' p^ = 52.3 

Pd = Po= 76-5 PQ = 50-5 Po^ = 22.1 

Pe = Pp = 67.5 ^, = ^ = 28.3 Ps = 18.5 

^ = 67.5 p, = py= 25.3 p^=. p^ = ^ 

Pg = 76.9 ^ = 25.1 p^ = 17.6 

Ph= pi= 73-5 ^« = 29.0 

pi = Pm= 69.3 Pv === Py = 28.2 

Diagrams with the volumes and pressures corresponding to 
this example are plotted in Fig. 46 with convenient vertical 
scales. Actual indicator-diagrams taken from the engine are 
given by Fig. 47. The events of the stroke come at slightly 
different piston positions on account of the irregularity due to 
the connecting-rod, and the drops and other fluctuations of 
pressure are gradual instead of sudden; moreover, there is con- 
siderable loss of pressure from the boiler to the engine, from one 
cylinder to another, and from the low-pressure cylinder to the 
condenser. Nevertheless the general forms of the diagrams are 
easily recognized, and all apparent erratic variations are 
accounted for. 

Designing Compound Engines. — The designer of compound 
and multiple-expansion engines should have at hand a well- 
systematized fund of information concerning the sizes, pro- 
portions, and powers of such engines, together with actual 
indicator-diagrams. He may then, by a more or less direct 
method of interpolation or exterpolation, assign the dimensions 
and proportions to a new design, and can, if deemed advisable, 
draw or determine a set of probable indicator-diagrams for the 
new engines. If the new design differs much from the engines 
for which he has information, he may determin'e approximate 
diagrams both for an actual engine from which indicator-dia- 
grams are at hand, and for the new design. He may then 
sketch diagrams for the new engine, using the approximate 



DESIGNING COMPOUND ENGINES 



179 



diagrams as a basis and taking a comparison of the approximate 
and actual diagrams from the engine already built, as a guide. 
It is convenient to prepare and use a table showing the ratios of 
actual mean effective pressures and approximate mean effective 
pressures. Such a table enables the designer to assign mean 
effective pressures to a cylinder of the new engine and to infer 
very closely what its horse-power will be. It is also very useful 
as a check in sketching probable diagrams for a new engine, 
which diagrams are not only useful in estimating the power of the 
new engine, but in calculating stresses on the members of that 
engine. 

A rough approximation of the power of an engine may be 
made by calculating the power as though the total or equivalent 
expansion took place in the low-pressure cylinder, neglecting/ 
clearance and compression. The power thus found is to be 
affected by a factor which according to the size and type of the 
engine may vary from 0.6 to 0.9 for compound engines and from 
0.5 to 0.8 for triple engines. Seaton and Rounthwaite * give the 
following table of multipHers for compound marine engines: 

MULTIPLIERS FOR FINDING PROBABLE M.E.P. COMPOTOTD 
.\ND TRIPLE MARINE ENGINES. 



Description of Engine. 



Receiver-compound, screw-engines 

Receiver-compound, paddle-engines 

Direct expansion 

Three-cylinder triple, merchant ships 

Three-cylinder triple, naval vessels 

Three-cylinder triple, gunboats and torpedo-boats 



Jacketed. 



0.67 to o. 73 



o . 64 to o. 68 
0.55 to 0.65 



Un jacketed. 



0.58 to Q.68 
0.55 to 0.65 
0.71 to 0.75 
0.60 to 0.66 



o . 60 to o. 67 



For example, let the boiler- pressure be 80 pounds by the gauge, 
or 94.7 pounds absolute; let the back-pressure be 4 pounds 
absolute; and let the total number of expansions be six, so that 
the volume of steam exhausted to the condenser is six times the 



* Pocket Book of Marine Engineering. 



l8o COMPOUND ENGINES 

volume admitted from the boiler. Neglecting the effect of clear- 
ance and compression, the mean effective pressure is 

94.7 X h + 94.7 X i log, f - 4 X I = 40.06 = M.E.P. 

If the large cylinder is 30 inches in diameter, and the stroke 
is 4 feet, the horse-power at 60 revolutions per minute is 

— ^ X 40.06 X 2 X 4 X 60 -^ 33000 = 412 H.P. 
4 

If the factor to be used in this case is 0.75, then the actual 
horse-power will be about 

0.75 X 400 = 300 H.P. 

Binary Engines. — Another form of compound engines using 
two fluids like steam and ether, was proposed by du Trembly * in 
1850, to extend the lower range of temperature of vapor-engines. 
At that time the common steam-pressure was not far from thirty 
pounds by the gauge, corresponding to a temperature of 250° F. 
If the back-pressure of the engine be assumed to be 1.5 pounds 
absolute (115° F.), the efficiency for Carnot's cycle would be 
approximately 

2t^O — 115 



250 + 460 



0.19. 



If, however, by the use of a more volatile fluid the result at 
lower temperature could be reduced to 65° F., the efficiency 
could be increased to 

250 - 65 , 

-^ ^ = 0.26. 

250 -f 460 

At the present time when higher steam-pressures are common, 
the comparison is less favorable. Thus the temperature of 
steam at 150 pounds by the gauge is 365° F., so that with 1.5 

* Manuel du Conducteur des Machines a Vaporous comhinees au Machines 
Binaires, also Rankine Steam Engine, p. 444. 



BINARY ENGINES l8l 

pounds absolute (or 1 1 5° F. ) for the back-pressure the efficiency 
for Carnot 's cycle is 

^6s — lis 

365 + 460 

and for a resultant temperature of 65° F., the efficiency would be 

-^-^ ^ = 0.36. 

365 + 460 

If a like gain of economy could be obtained in practice, it 
would represent a saving of 17 per cent, which would be well 
worth while. Further discussion of this matter of economy will 
be given in Chapter XI, in connection with experiments on 
binary engines using steam and sulphur-dioxide. 

The practical arrangement of a binary engine substitutes for, 
the condenser an appliance having somewhat the same form as 
a tubular surface-condenser, the steam being condensed on the 
outside of the tubes and withdrawn in the form of water of con- 
densation at the bottom. Through the tubes is forced the 
more volatile fluid, which is vaporized much as it would be in a 
"water-tube" boiler. The vapor is then used in a cylinder 
differing in no essential from that for a steam-engine, and in turn 
is condensed in a surface-condenser which is cooled with water 
at the lowest possible temperature. 

An ideal arrangement for a binary engine avoiding the use of 
air-pumps would appear to be the combination of a compound 
non-condensing steam-engine with a third cylinder on the binary 
system which should have for its working substance a fluid that 
would give a convenient pressure at 212° F., and a pressure 
somewhat above the atmosphere at 60° F. There is no known 
fluid that gives both these conditions; thus ether at 212° F. gives 
a pressure of about 96 pounds absolute, but its boiling-point at 
atmospheric pressure is 94° F., consequently it would from 
necessity require a vacuum and an air-pump unless the ether 
could be entirely freed from air, and leakage into the vacuum 
space entirely prevented. Sulphur-dioxide gives a pressure of 41 



l82 COMPOUND ENGINES 

pounds absolute at 60° F., so that it can always be worked at a 
pressure above the atmosphere; but 212° F. would give an incon- 
venient pressure, and in practice it has been found convenient 
to run the steam-engine with a vacuum of 22 inches of mercury 
or about 4 pounds absolute, which gives a temperature of 155° F., 
at which sulphur-dioxide has a pressure of 180 pounds per square 
inch by the gauge. 

The attempt of du Trembly to use ether for the second fluid 
in a binary engine did not result favorably, as 'his fuel-con- 
sumption was not less than that of good engines of that time, 
which appears to indicate that he could not secure favorable 
conditions. 



CHAPTER X. 

TESTING STEAM-ENGINES. 

The principal object of tests of steam-engines is to determine 
the cost of power. Series of engine tests are made to 
determine the effect of certain conditions, such as superheating 
and steam-jackets, on the economy of the engine. Again, tests 
may be made to investigate the interchanges of heat between the 
steam and the walls of the cylinder by the aid of Hirn's analysis, 
and thus find how certain conditions produce effects that are 
favorable or unfavorable to economy. 

The two main elements of an engine test are, then, the meas- 
urement of the power developed and the determination of the 
cost of the power in terms of thermal units, pounds of steam, or 
pounds of coal. Power is most commonly measured by aid of 
the steam-engine indicator, but the power delivered by the 
engine is sometimes determined by a dynamometer or a friction 
brake; sometimes, when an indicator cannot be used conven- 
iently, the dynamic or brake power only is determined. When 
the engine drives a dynamo-electric generator the power applied 
to the generator may be determined electrically, and thus the 
power delivered by the engine may be known. 

When the cost of power is given in terms of coal per horse- 
power per hour, it is sufficient to weigh the coal for a definite 
period of time. In such case a combined boiler and engine test 
is made, and all the methods and precautions for a careful boiler 
test must be observed. The time required for such a test 
depends on the depth of the fire on the grate and the rate of 
combustion. For factory boilers the test should be twenty-four 
hours long if exact results are desired. 

When the cost of power is stated in terms of steam per horse- 
power per hour, one of two methods may be followed. When 

183 



l84 TESTING STEAM-ENGINES 

the engine has a surface-condenser the steam exhausted from the 
engine is condensed, collected, and weighed. One hour is 
usually sufficient for tests under favorable conditions; shorter 
intervals, ten or fifteen minutes, give fairly uniform results. 
The chief objection to this method is that the condenser is liable 
to leak water at the tube packings. Under favorable conditions 
the results of tests by this method and by determining the feed- 
water supplied to the boiler are substantially the same. In tests 
on non-condensing and on jet-condensing engines the steam- 
consumption is determined by weighing or measuring the feed- 
water supplied to the boiler or boilers that furnish steam to the 
engine. Steam used for any other purpose than running the 
engine, for example, for pumping, heating, or making determi- 
nations of the quality of the steam, must be determined and 
allowed for. The most satisfactory way is to condense and 
weigh such steam; but small quantities, as for determining 
quality by a steam calorimeter, may be gauged by allowing it to 
flow through an orifice. Tests which depend on measuring the 
feed- water should be long enough to minimize the effect of the 
uncertainty of the amount of water in a boiler corresponding to 
an apparent height of water in a water-gauge; for the apparent 
height of the water-level depends largely on the rate of vaporiza- 
tion and the activity of convection currents. 

When the cost of power is expressed in thermal units it is 
necessary to measure the steam-pressure, the amount of moisture 
in the steam supplied to the cylinder, and the temperature of the 
condensed steam when it leaves the condenser. If steam is used 
in jackets or reheaters it must be accounted for separately. 
But it is customary in all engine tests to take pressures and 
temperatures, so that the cost -may usually be calculated in 
thermal units, even when the experimenter is content to state it 
in pounds of steam. 

For a Hirn's analysis it is necessary to weigh or measure the 
condensing water, and to determine the temperatures at admis- 
sion to and exit from the condenser. 

Important engines, with their boilers and other appurtenances, 



TESTING STEAM-ENGINES 185 

are commonly built under contract to give a certain economy, 
and the fulfilment of the terms of a contract is determined by a 
test of the engine or of the whole plant. The test of the entire 
plant has the advantage that it gives, as one result, the cost of 
power directly in coal ; but as the engine is often watched with more 
care during a test than in regular service, and as auxiliary duties, 
such as heating and banking fires, are frequently omitted from 
such an economy test, the actual cost of power can be more 
justly obtained from a record of the engine in regular service, 
extending for weeks or months. The tests of engine and boilers, 
though made at the same time, need not start and stop at the 
same time, though there is a satisfaction in making them 
strictly simultaneous. This requires that the tests shall be long 
enough to avoid drawing the fires at beginning and end of the 
boiler test. 

In anticipation of a test on an engine it must be run for some 
time under the conditions of the test, to eliminate the effects of 
starting or of changes. Thus engines with steam-jackets are 
commonly started with steam in the jackets, even if they are to 
run with steam excluded from the jackets. An hour or more 
must then be allowed before the effect of using steam in the 
jackets will entirely pass away. An engine without steam- 
jackets, or with steam in the jackets, may come to constant 
conditions in a fraction of that time, but it is usually well to 
allow at least an hour before starting the test. 

It is of the first importance that all the conditions of a test 
shall remain constant throughout the test. Changes of steam- 
pressure are particularly bad, for when the steam-pressure rises 
the temperature of the engine and 'all parts affected by the steam 
must be increased, and the heat required for this purpose is 
charged against the performance of the engine; if the steam- 
pressure falls a contrary effect will be felt. In a series of tests 
one clement at a time should be changed, so that the effect of 
that element may not be confused by other changes, even though 
such changes have a relatively small effect. It is, however, of 
more importance that steam-pressure should remain constant 



1 86 TESTING STEAM-ENGINES 

than that all tests at a given pressure should have identically the 
same steam-pressure, because the total heat of steam varies more 
slov^^Iy than the temperature. 

All the instruments and apparatus used for an engine test 
should be tested and standardized either just before or just 
after the test; preferably before, to avoid annoyance when any 
instrument fails during the test and is replaced by another. 

Thermometers. — Temperatures are commonly measured by 
aid of mercurial thermometers, of which three grades may be 
distinguished. For work resembling that done by the physicist 
the highest grade should be used, and these must ordinarily be 
calibrated, and have their boiling- and freezing-points deter- 
mined by the experimenter or some qualified person; since the 
freezing-point is liable to change, it should be redetermined when 
necessary. For important data good thermometers must be used, 
such as are sold by reliable dealers, but it is preferable that they 
should be calibrated or else compared with a thermometer that 
is known to be reliable. For secondary data or for those requir- 
ing little accuracy common thermometers with the graduation 
on the stem may be used, but these also should have their errors 
determined and allowed for. Thermometers with detachable 
scales should be used only for crude work. 

Gauges. — Pressures are commonly measured by Bourdon 
gauges, and if recently compared with a correct mercury column 
these are sufficient for engineering work. The columns used 
by gauge-makers are sometimes subject to minor errors, and are 
not usually corrected for temperature. It is important that 
such gauges should be frequently retested. 

Dynamometers. — The standard for measurement of power 
is the friction-brake. For smooth continuous running it is 
essential that the brake and its band shall be cooled by a stream 
of water that does not come in contact with the rubbing sur- 
faces. Sometimes the wheel is cooled by a stream of water cir- 
culating through it, sometimes the band is so cooled, or both may 
be. A rubbing surface which is not cooled should be of non- 
conducting material. If both rubbing surfaces are metallic they 



INDICATORS 187 

must be freely lubricated with oil. An iron wheel running in a 
band furnished with blocks of wood requires little or no lubri- 
cation. 

To avoid the increase of friction on the brake- bearings due 
to the load applied at a single brake-arm, two equal arms may 
be used with two equal and opposite forces applied at the ends 
to form a statical couple. 

With care and good workmanship a friction- brake may be 
made an instrument of precision sufficient for physical investi- 
gations, but with ordinary care and workmanship it will give 
results of sufficient accuracy for engineering work. 

An engine which drives an electric-generator may readily have 
the dynamic or brake- power determined from the electric out- 
put, provided that the efficiency of the generator is properly 
determined. 

The only power that can be measured for a steam-turbine is 
the dynamic or brake-power; when connected with an electric- 
generator this involves no difficulty. For marine propulsion it 
is customary to determine the power of steam-turbines by some 
form of torsion-metre applied to the shaft that connects the 
turbine to the propeller. This instrument measures the angle 
of torsion of the shaft while running, and consequently, if the 
modulus of elasticity has been determined, gives a positive 
determination of the power delivered to the propeller. Under 
favorable conditions a torsion-metre may have an error of not 
more than one per cent. 

Indicators. — The most important and at the same time the 
least satisfactory instrument used in engine-testing is the indi- 
cator. Even when well made and in good condition it is liable 
to have an error which may amount to two per cent when used 
at moderate speeds. At high speeds, three hundred revolutions 
per minute and over, it is likely to have two or three times as 
much error. As a rule, an indicator cannot be used at more 
than four hundred revolutions per minute. 

The mechanism for reducing the motion of the crosshead of 
the engine and transferring it to the paper drum of an indicator 



l88 TESTING STEAM-ENGINES 

should be correct in design and free from undue looseness. It 
should require only a very short cord leading to the paper drum, 
because all the errors due to the paper drum are proportional to 
the length of the cord and may be practically eliminated by 
making the cord short. 

The weighing and recording of the steam-pressure by the indi- 
cator-piston, pencil-motion, and pencil are affected by errors 
which may be classified as follows : 

1. Scale of the spring. 

2. Design of the pencil-motion. 

3. Inertia of moving parts. 

4. Friction and backlash. 

Good indicator-springs, when tested by direct loads out of 
the indicator, usually have correct and uniform scales; that is, 
they collapse under pressure the proper amount for each load 
applied. When enclosed in the cylinder of an indicator the 
spring is heated by conduction and radiation to the temperature 
of the cylinder, and that temperature is sensibly equal to the 
mean temperature in the engine-cylinder. But a spring is appre- 
ciably weaker at high temperatures, so that when thus enclosed 
in the indicator-cylinder, it gives results that are too large; the 
error may be two per cent or more. 

Outside spring-indicators avoid this difficulty and are to be 
preferred for all important work. They have only one disad- 
vantage, in that the moving parts are heavier, but this may be 
overcome by increasing the area of the piston from half a square 
inch to one square inch. 

The motion of the piston of the indicator is multiplied five 
or six times by the pencil-motion, which is usually an approx- 
imate parallel motion. Within the proper range of motion 
(about two inches) the pencil draws a line which is nearly 
straight when the paper drum is at rest, and it gives a nearly 
uniform scale provided that the spring is uniform. The errors 
due to the geometric design of this part of the indicator are 
always small. 



INDICATORS 189 

When steam is suddenly let into the indicator, as at admission 
to the engine-cylinder, the indicator-piston and attached parts 
forming the pencil-motion are set into vibration, with a natural 
time of vibration depending on the stiffness of the spring. A 
weak spring used for indicating a high-speed engine may throw 
the diagram into confusion, because the pencil will give a few 
deep undulations which make it impossible to recognize the 
events of the stroke of the engine, such as cut-off and release. 
A stiffer spring will give more rapid and less extensive undu- 
lations, which will be much less troublesome. As a rule, when 
the undulations do not confuse the diagram the area of the dia- 
gram is but little affected by the undulations due to the inertia 
of the piston and pencil-motion. 

The most troublesome errors of the indicator are due 
to friction and backlash. The various joints at the piston 
and in the pencil-motion are made as tight as can be without 
undue friction, but there is always some looseness and some 
friction at those joints. There is also some friction of the piston 
in the cylinder and of the pencil on the paper. Errors from this 
source may be one or two per cent, and are liable be excessive 
unless the instrument is used with care and skill. A blunt 
pencil pressed up hard on the paper will reduce the area of the 
diagram five per cent or more; on the other hand, a medium 
pencil drawing a faint but legible line will affect the area very 
little. Any considerable friction of the piston of the indicator 
will destroy the value of the diagram. 

Errors of the scale of the spring can be readily determined and 
investigated by loading the spring with known weights, when 
properly supported, out of the indicator. This method is prob- 
ably sufficient for outside spring indicators. Those that have 
the spring inside the cylinder are tested under steam pressure, 
measuring the pressure either by a gauge or a mercury column. 
Considerable care and skill are required to get good results, 
especially to avoid excessive friction of the piston as it remains 
at rest or moves slowly in the cylinder. It must be borne in 
mind that the indicator cylinder heats readily when subjected to 



I go TESTING STEAM-ENGINES 

progressively higher steam pressures, but that it parts with heat 
slowly, and that consequently tests made with falling steam 
pressures are not valuable. 

Scales. — ' Weighing should be done on scales adapted to the 
load ; overloading leads to excessive friction at the knife-edges and 
to lack of delicacy. Good commercial platform scales, when 
tested with standard weights, are sufficient for engineering work. 

Coal and ashes are readily weighed in barrows, for which the 
tare is determined by weighing empty. Water is weighed in 
barrels or tanks. The water can usually be pumped in or 
allowed to run in under a head, so that the barrel or tank can be 
filled promptly. Large quick-opening valves must be used to allow 
the water to run out quickly. As the receptacle will seldom drain 
properly, it is not well to wait for it to drain, but to close the 
exit- valve and weigh empty with whatever small amount of water 
may be caught in it. Neither is it well to try to fill the receptacle 
to a given weight, as the jet of water running in may affect the 
weighing. With large enough scales and tanks the largest 
amounts of water used for engine tests may be readily handled. 

Measuring Water. — When it is not convenient to weigh water 
directly, it may be measured in tanks or other receptacles of 
known volume. Commonly two are used, so that one may 
fill while the other is emptied. The' volume of a receptacle may 
be calculated from its dimensions, or may be determined by 
weighing in water enough to fill it. When desired a receptacle 
may be provided with a scale showing the depth of the water, 
and so partial volumes can be determined. A closed recep- 
tacle may be used to measure hot water or other fluids. 

Water-Meters of good make may be used for measuring water 
when other methods are not applicable, provided they are tested 
and rated under the conditions for which they are used, taking 
account of the amount and temperature of the water measured. 
Metres are most convenient for testing marine engines because 
water cannot be weighed at sea on account of the motion of the 
ship, and arrangements for measuring water in tanks are expen- 
sive and inconvenient. For such tests the metre may be placed 



THROTTLING-CALORIMETER 



191 



on a by-pass through which the feed-water from the surface- 
condenser can be made to pass by closing a valve on the direct 
line of feed-pipe. If necessary the metre can be quickly shut 
ofif and the direct line can be opened. The chief uncertainty in 
the use of a metre is due to air in the water; to avoid error from 
this source, the metre should be frequently vented to allow air 
to escape without being recorded by the metre. 

Weirs and Orifices. — So far as possible the use of weirs and 
orifices for water during engine tests should be avoided, for, in 
addition to the uncertainties unavoidably connected with such 
hydraulic measurements, difficulties are liable to arise from the 
temperature of the water and from the oil in it. A very little oil 
is enough to sensibly affect the coefficient for a weir or orifice. 
The water flowing from the hot-well of a jet-condensing engine 
is so large in amount that it is usually deemed advisable to 
measure it on a w^eir; the effect of temperature and oil is less 
than when the same method is used for measuring condensed 
steam from a surface-condenser. 

Priming-Gauges. — • When superheated steam is supplied to an 
engine it is sufficient to take the temperature of the steam in the 
steam-pipe near the engine. When moist steam is used the amount 
of moisture must be determined by a separated test. Origi- 
nally such tests were made by some form of calorimeter, and 
that name is now commonly attached to certain devices which 
are not properly heat-measurers. Three of these will be men- 
tioned : (i ) the throttling-calorimeter, which can usually be applied 
to all engine tests; (2) the separating-calorimeter, which can be 
applied when the steam is wet; and (3) the Thomas electric calor- 
imeter, intended for use with steam-turbines to determine the 
moisture in steam at any stage of the turbine whatever may be 
the pressure or quality of the steam. 

Throttling-Calorimeter. — A simple form of calorimeter, 
devised by the author, is shown by Fig. 48, where ^4 is a 
reservoir about 4 inches in diameter and about 12 inches long 
to which steam is admitted through a half-inch pipe b, with a 
throttle- valve near the reservoir. Steam flows away through an 



ig: 



TESTING STEAM-ENGINES 



e ^==^ 





inch pipe d. At / is a gauge for measuring the pressure, and at 
e there is a deep cup for a thermometer to measure the temper- 
ature. The boiler-pressure may be taken 
from a gauge on the main steam-pipe 
near the calorimeter. It should not be 
taken from a pipe in which there is a 
^iltTl I rapid flow of steam as in the pipe ft, 

since the velocity of the steam will affect 
the gauge-reading, making it less than the 
real pressure. The reservoir is wrapped 
with hair-felt and lagged with wood to 
reduce radiation of heat. 

When a test is to be made, the valve on 
the pipe d is opened wide (this valve is 
frequently omitted), and the valve at h is 
opened wide enough to give a pressure of 
live to fifteen pounds in the reservoir. 
Readings are then taken of the boiler- 
gauge, of the gauge at /, and of the thermometer at e. It is well to 
wait about ten minutes after the instrument is started before taking 
readings so that it may be well heated. Let the boiler-pressure 
be ^, and let r and q be the latent heat and heat of the liquid 
corresponding. Let p^ be the pressure in the calorimeter, r^ the 
heat of vaporization, q^ the heat of the liquid, and t^ the tempera- 
ture of saturated steam at that pressure, while i^ is the tempera- 
ture of the superheated steam in the calorimeter. Then 



Fig. 48. 



. ^ _ ^1 + ^, + c^ {is - t,) - q 



(152) 



Example. — The following are the data of a test made with 
this calorimeter: 

Pressure of the atmosphere .... 14.8 pounds; 
Steam-pressure by gauge .... 69.8 " 
Pressure in the calorimeter, gauge . 12.0 " 

Temperature in the calorimeter . . 268°. 2 F. 



THROTTLING-CALORIMETER 



193 



Specific heat of superheated steam for the condition of the 
test 0.48. 

943.8 + 212.7 + Q-4^ (268.2 — 243.9) "~ 2^5-9 _ 
892.3 

Per cent of priming, 1.2. 



X = 



0.988; 



A little consideration shows that this type of calorimeter 
can be used only when the priming is not excessive; otherwise 
the throttling will fail to superheat the steam, and in such case 
nothing can be told about the condition of the steam either before 
or after throttling. To find this limit for any pressure 4 may be 
made equal to t^ in equation (152); that is, we may assume that 
the steam is just dry and saturated at that limit in the calorimeter. 
Ordinarily the lowest convenient pressure in the calorimeter is 
the pressure of the atmosphere, or 14.7 pounds to the square inch. 
The table following has been calculated for several pressures in 
the manner indicated. It shows that the limit is higher for higher 
pressures, but that the calorimeter can be applied only where 
the priming is moderate. 

When this calorimeter is used to test steam supplied to a 
condensing-engine the limit may be extended by connecting the 
exhaust to the condenser. For example, the limit at 100 pounds 
absolute, with 3 pounds absolute in the calorimeter, is 0.064 
instead of 0.040 with atmospheric pressure in the calorimeter. 



LIMITS OF THE THROTTLING-CALORIMETER. 



Pressure. 








Priming. 


Absolute. 


Gauge. 


300 


285.3 


0.077 


250 


235-3 


0.070 


200 


185.3 


0.061 


175 


160.3 


0.058 


150 


135-3 


0.052 


125 


no. 3 


0.046 


100 


l^-^ 


0.040 


75 


60.3 


0.032 


50 


35-3 


0.023 



194 TESTING STEAM-ENGINES 

In case the calorimeter is used near its limit — that is, when 
the superheating is a few degrees only — it is essential that the 
thermometer should be entirely reliable; otherwise it might 
happen that the thermometer should show superheating when 
the steam in the calorimeter was saturated or moist. In any 
other case a considerable error in the temperature will produce 
an inconsiderable effect on the result. Thus at loo pounds 
absolute with atmospheric pressure in the calorimeter, io° F. of 
superheating indicates 0.035 priming, and 15° F. indicates 0.032 
priming. So also a slight error in the gauge-reading has little 
effect. Suppose the reading to be apparently 100.5 pounds 
absolute instead of 100, then with 10° of superheating the prim- 
ing appears to be 0.033 instead of 0.032. 

It has been found by experiment that no allowance need be 
made for radiation from this calorimeter if made as described, 
provided that 200 pounds of steam are run through it per hour. 
Now this quantity will flow through an orifice one-fourth of an 
inch in diameter under the pressure of 70 pounds by the gauge, 
so that if the throttle-valve be replaced by such an orifice the 
question of radiation need not be considered. In such case a 
stop- valve will be placed on the pipe to shut off the calorimeter 
when not in use; it is opened wide when a test is made. If an 
orifice is not provided the throttle- valve may be opened at first 
a small amount, and the temperature in the calorimeter noted; 
after a few minutes the valve may be opened a trifle more, where- 
upon the temperature may rise, if too little steam was used at 
first. If the valve is opened little by little till the temperature 
stops rising, it will then be certain that enough steam is used to 
reduce the error from radiation to a very small amount. 

Separating-Calorimeter. — If steam contains more than 
three per cent of moisture the priming may be determined by 
a good separator which will remove nearly all the moisture. 
It remains to measure the steam and water separately. The 
water may be best measured in a calibrated vessel or receiver, 
while the steam may be condensed and weighed, or may be 
gauged by allowing it to flow through an orifice of known size. 



THE THOMAS ELECTRIC CALORIMETER 



195 



A form of separating-calorimeter devised by Professor Carpenter * 
is shown by Fig. 49. 

Steam enters a space at the top 
which has sides of wire gauze and a 
convex cup at the bottom. The water 
is thrown against the cup and finds its 
way through the gauze into an inside 
chamber or receiver and rises in a 
water-glass outside. The receiver is 
caUbrated by trial, so that the amount of 
water may be read directly from a gradu- 
ated scale. The steam meanwhile passes 
into the outer chamber which surrounds 
the inner receiver and escapes from an 
orifice at the bottom. The steam may 
be determined by condensing, collecting, 
and weighing it; or it may be calculated 
from the pressure and the size of the 
orifice. When the steam is weighed 
there is no radiation error, since the 

inner chamber is protected by the steam in the outer chamber. 
This instrument may be guarded against radiation by wrapping 
and lagging, and then if steam enough is used the radiation will 
be insignificant, just as was found to be the case for the 
throttling-calorimeter. 

The Thomas Electric Calorimeter. — The essential feature of this 
instrument (Fig. 50) is the drying and superheating of the steam 
by a measured amount of electric energy. Steam is admitted 
at B and passes through numerous holes in a block of soapstone 
which occupies the middle of the instrument; these holes are 
partially filled with coils of German silver wire which are heated 
by an electric current that enters and leaves at the binding- 
screws. The steam emerges dry or superheated at the upper 
part of the chamber and passes down through wire gauze, which 
surrounds the central escape pipe; this central pipe surrounds 

* Trans. Am. Soc. Mech. Engs., vol. xvii, p. 608. 




Fig. 49. 



196 



TESTING STEAM-ENGINES 



the thermometer cup, and leads to the exit at the top, which has 
two orifices, either of which may be piped to a condenser or 

elsewhere. 

To use the instrument it is 
properly connected by a sampling- 
tube to the space from which 
steam is drawn, and valves are 
adjusted to supply a convenient 
amount of steam which is assumed 
to be uniform for steady pressure; 
this last is a matter of some im- 
portance. 

The current of electricity is 
then adjusted to dry the steam; 
this may be determined by noting 
the temperature by the thermom- 
eter in the central thermometer 
cup, because that thermometer 
will show a slight rise corres- 
ponding to a very small degree 
of superheating which is sufficient 
to indicate the disappearance of 
moisture, but not enough to affect 
the determination of quality by 
the instrument. The wire gauze 
surrounding the thermometer is an essential feature of this 
operation, as it insures the homogeneity of the steam, which, 
without the gauze, would be likely to be a mixture of super- 
heated steam and moist steam. Readings are taken of the 
proper electrical instruments from which the electrical energy 
imparted can be determined in watts; let this energy required to 
dry the steam be denoted by E^. Now let the electric current be 
increased till the steam is superheated 30°, and let E^ be the 
increase of electric input which is required to superheat the 
steam. 

If W is the weight of steam flowing per hour through the 




Fig. 50. 



THE THOMAS ELECTRIC CALORIMETER 



197 



instrument under the first conditions, the weight when super- 
heated will be CW, where C is a factor less than unity which 
has been determined by exhaustive tests on the instrument. 
The amount of electric energy required to superheat one pound 
of steam 30° from saturation at various pressures has also been 
determined and may be represented by 5; this constant has been 
so determined as to include an allowance for radiation, and is 
more convenient than the specific heat of superheated steam, in 
this place. Making use of the factors C and S, we may write 

E, = CSW, otW = ^, 

which affords a means of eliminating the weight of steam used; 
this is an important feature in the use of the instrument. 

Returning now to the first condition of the instrument when 
steam is dried by the application of E^ watts of electric energy, 
we have for the equivalent heat 

3.42 E^; 

and dividing by the expression for the weight of steam flowing 
per hour, we have for the heat required to dry one pound of 
steam 

where r is the heat of vaporization and i — jc is the amount of 
water in one pound of moist steam. 

Solving the above equation for x, we have 

3.42 CS E, 
X - I -^^ -^. 

If desired, the constant factors may be united into one term, and 
the equation may be written 

_KE^ 
r e/ 

With each instrument is furnished a diagram giving values of 
K for all pressures, so that the use of the instrument involves 



198 TESTING STEAM-ENGINES 

only two readings of a wattmeter and the application of the above 
simple equation. 

For example, suppose that the use of the instrument in a 
particular case gave the values E^ = 240, and E^ = 93.0 for 
the absolute pressure 100 pounds per square inch. The value 
of K from the diagram is 54.2, and r from the steam- tables is 884, 
consequently 

^4.2 240 „ 

884 93.0 

Method of Sampling Steam. — It is customary to take a sample 
of steam for a calorimeter or priming-gauge through a small 
pipe leading from the main steam-pipe. The best method of 
securing a sample is an open question; indeed, it is a question 
whether we ever get a fair sample. There is no question but 
that the composition of the sample is correctly shown by any of 
the calorimeters described, when the observer makes tests with 
proper care and skill. It is probable that the best way is to 
take steam through a pipe which reaches at least halfway across 
the main steam-pipe, and which is closed at the end and drilled 
full of small holes. It is better to have the sampling- pipe at 
the side or top of the main, and it is better to take a sample 
from a pipe through which steam flows vertically upward. The 
sampling-pipe should be short and well wrapped to avoid 
radiation. 



CHAPTER XI. 

INFLUENCE OF THE CYLINDER WALLS. 

In this chapter a discussion will be given of the discrepancy 
between the theory of the steam-engine as detailed in the previous 
chapter, and the actual performance as determined by tests on 
engines. It was early evident that this discrepancy was due 
to the interference of the metal of the cylinder walls which 
abstracted heat from the steam at high pressure and gave it out 
at low pressure. In consequence there followed a long struggle 
to determine precisely what action the walls exerted and how to 
allow for that action in the design of new engines. The first 
part has been accomplished; we can determine to a nicety the 
influence of the cylinder walls for any engine already built and 
tested; but as yet all attempts to systematize the information 
derived from such tests in such a manner that it can be used 
in the design of new engines has been utterly futile. Conse- 
quently the discussion in this chapter is important mainly 
in that it allows us to understand the real action of certain 
devices that are intended to improve the economy of engines, 
and to form a just opinion on the probability of future im- 
provements. 

As soon as the investigations by Clausius and Rankine 
and the experiments by Regnault made a precise theory of 
the steam engine possible, it became evident that engines used 
from quarter to half again as much steam as the adiabatic 
theory indicated, and in particular that expansion down to 
the back-pressure was inadvisable. An early and a satis- 
factory exposition of these points was made by Isherwood 
after his tests on the U. S. S. Michigan^ which are given in 
Table III. 



199 



200 



INFLUENCE OF THE CYLINDER WALLS 



Table III. 

TESTS ON THE ENGINE OF THE U. S. S. MICHIGAN. 

CYLINDER DIAMETER, 36 INCHES; STROKE, 8 FEET. 

By Chief-Engineer Isherwood, Researches in Experimental Steam 
Engineering. 



Duration, hours 

Cut-off 

Revolutions per minute 

Boiler-pressure, pounds per sq in. above 

atmosphere 

Barometer, inches of mercury 

Vacuum, inches of mercury 

Steam per horse-power per hour, pounds 
Per cent of water in cylinder at release 



I. 


II 




III. 

72 


IV. 

72 


V. 

72 


VI. 

72 


72 


72 


II/I2 


7/10 


4/9 


3/10 


1/4 


1/6 


20.6 


i5-t> 


17-3 


13-7 


13-9 


II. 2 


21.0 


19 -5 


21.0 


21.0 


21.0 


21.0 


30.1 


2Q 


8 


29.7 


30.1 


29-9 


29-9 


26.5 


26 


I 


26.3 


25.8 


25.8 


25.6 


38.0 


2>2> 


8 


32.7 


34.7 


34.5 


36.8 


10.7 


15 


3 


27.2 


41.7 


39-^ 


42.1 



72 
4/45 
14. 1 

22.0 

29.9 
24.1 
41.4 

45-1 



U.S. g. MICHIGAN 

Abscissae per cents of cut off 
Ordinates pounds of steam 
per horse power per hour. 



In the first place the best economy for this engine w^as 32.7 
pounds instead of 26.5 pounds as calculated by the expression 

60 X 33000 

778 (^1 + g, ~ oc^r.^ - g,) 

deduced on page 141 for the steam-consumption for a non-con- 
ducting engine with 
complete expansion. 
This result was ob- 
tained with cut-off at 
four-ninths of the 
stroke which gave a 
terminal pressure of 
one pound above the 
atmosphere. 

The manner of the 
variation of the steam 
consumption with the 
cut-off is clearly 
shown by Fig. 51, in 

which the fraction of stroke at cut-off is taken for abscissae and 

the steam-consumptions as ordinates. 




Fig. 



INFLUENCE OF THE CYLINDER WALLS 201 

To make the diagram clear and compact, the axis of abscissae 
is taken at 30 pounds of steam per horse-power per hour. An 
inspection of this diagram and of the figures in the table shows 
a regularity in the results which can be attained only when tests 
are made with care and skill. The only condition purposely 
varied is the cut-off; th^only condition showing important acci- 
dental variation is the vacuum, and consequently the back- 
pressure in the cylinder. To allow for the small variations in 
the back-pressure Isherwood changed the mean effective pressure 
for each test by adding or subtracting, as the case might require, 
the difference between the actual back- pressure and the mean 
back- pressure of 2.7 pounds per square inch, as deduced from 
all the tests. 

An inspection of any such a series of tests having a wide range 
of expansions will show that the steam-consumption decreases 
as the cut-off is shortened till a minimum is reached, usually at 
^ to B^ stroke ; any further shortening of the cut-off will be accom- 
panied by an increased steam-consumption, which may become 
excessive if the cut-off is made very short. Some insight into 
the reason for this may be had from the per cent of water in the 
cylinder, calculated from the dimensions of the cylinder and the 
pressures in the cylinder taken from the indicator-diagram. 
The method of the calculation will be given in detail a little later 
in connection with Hirn's analysis. It will be sufficient now to 
notice that the amount of water in the cylinder of the engine of 
the Michigan at release increased from 10.7 per cent for a cut-off 
at i^ of the stroke to 45.1 per cent for a cut-off at 4*3- of the 
stroke. Now all the water in the cylinder at release is vaporized 
during the exhaust, the heat for this purpose .being abstracted 
from the cylinder walls, and the heat thus abstracted is wasted, 
without any compensation. The walls may be warmed to some 
extent in consequence of the rise of pressure and temperature 
during compression, but by far the greater part of the heat 
abstracted during exhaust must be supplied by the incoming 
.steam at admission. There is, therefore, a large condensation 
of steam during admission and up to cut-off, and the greater part 



202 INFLUENCE OF THE CYLINDER WALLS 

of the Steam thus condensed remains in the form of water and 
does little if anything toward producing work. This may be 
seen by inspection of the table of results of Dixwell's tests on 
page 270. With saturated steam and with cut-off at 0.217 of the 
stroke, 52.2 per cent of the working substance in the cylinder 
was water. Of this 19.8 per cent was reevaporated during ex- 
pansion, and 32.4 per cent remained at release to be reevaporated 
during exhaust. When the cut-off was lengthened to 0.689 of 
the stroke, there was 27.9 per cent of water at cut-off and 23.9 
per cent at release. The statement in percentages gives a 
correct idea of the preponderating influence of the cylinder walls 
when the cut-off is unduly shortened; it is, however, not true 
that there is more condensation with a short than with a long 
cut-off. On the contrary, there is more water condensed in 
the cylinder when the cut-off is long, only the condensation 
does not increase as fast as do the weight of steam supplied to 
the cylinder and the work done, and consequently the conden- 
sation has a less effect. 

Graphical Representation. — The divergence of the actual 

expansion line from the 
adiabatic line can be 
shown in a striking manner 
by plotting the former on 
the temperature-entropy 
diagram as shown in 
Fig. 53 which is con- 
^'°" ^^' structed from the indicator- 

diagram in Fig. 52, shown with the axes of zero pressure and 
zero volume drawn in the usual manner, allowing for clearance 
and for the pressure of the atmosphere. 

In order to undertake this construction the weight of steam 
per stroke W as determined from the test of the engine during 
which the diagrams were taken, must be determined, and the 
weight of steam W^ caught in the clearance must be computed 
from the pressure and volume/, the beginning of compression. 
The dry steam line (Fig. 52) is drawn by the following process: 



b 


n 




,,^^^%&~— . 



GRAPHICAL REPRESENTATION 203 

a line ae is drawn at a convenient pressure, and on it is laid off 
the volume oi W -\- W ^ pounds of dry steam as determined 
from the steam-table to the proper scale of the drawing. Thus 
if Sg is the specific volume of the steam at the pressure p^ the 
volume of steam present if dry and saturated would be 

{W + W^) Se. 

But the length of the diagram L, in inches is proportional to 
the- piston displacement D in cubic feet. The latter is obtained 
by multiplying the area of the piston in square feet by its stroke 
in feet. For the crank end the net area of the piston is to be used, 
allowing for the piston-rod. Consequently the proper abscissa, 

representing the volume is obtained by multiplying by - , giving 

(W + W,) L 
D 
and of this all except 5 is a constant for which a numerical result 
can be found. 

The diagram shown by Fig. 52 was taken from the head end 
of the high-pressure cylinder of an experimental engine in the 
laboratory of the Massachusetts Institute of Technology. The 
value oiW+ W ^ was found to be 0.075 ^^ ^ pound; the piston 
displacement was 1.102 cubic feet, and the length of the diagram 
was 3.69 inches; consequently 

^---=0.251. 

The line ae was drawn at 90 pounds absolute at which s = 4.86 
cubic feet; the length of the line ae was consequently 

0.251 X 4.86 = 1.22 inch. 
Neglecting the volume of the water present, the volume of 
steam actually present bore the same ratio to the volume of the 
steam when saturated, that ac had to ae. This gave in the figure 
at c 

ac 0.04 
x,= — = -^^ = 0.771. 
ae I. 219 



204 



INFLUENCE OF THE CYLINDER WALLS 



To plot the point e on the temperature-entropy diagram, 
^ig- 53> we may find the temperature at 90 pounds absolute, 
namely, 320° F., and on a line with that temperature as an ordi- 
nate we may interpolate between the lines for constant values 

of X. Other points can 
be drawn in a like man- 
ner, and the curve eg can 
be sketched in; showing 
that the steam continues 
to yield heat to the cylin- 
der walls from cut-off till c 
is reached on Fig. 52, and 
perhaps a trifle longer. 
Beyond c the steam^ re- 
ceives heat from the walls 
until exhaust opens. 
Fig. 52, by drawing the 
The point d can be 




Fig. 53. 



The same feature is exhibited in 
adiabatic line xdn from the point of cut-off. 
located by multiplying the length ae, which represents the volume 
of steam in the cylinder when dry by the value of x after adia- 
batic expansion from the point of cut-off n. This point n is 
readily included in the preceding investigation, so that x^ can be 
determined. Locating n on the temperature-entropy diagram, 
Fig. 53, we may draw through it a Vertical constant entropy line 
and note where it cuts the lines corresponding to the pressure 
lines like ae in Fig. 52, and interpolate for the values of x. 
For example, the entropy at n in Fig. 53 appears to be 1.36, 
and at 320° F., which corresponds to 90 pounds, this entropy 
line gives by interpolation 0.78, so that the length of ad is 

0.78 X 1.22 = 0.95. 

In this discussion no attempt is made to distinguish the moisture 
which may be in contact with the wall from the remainder of 
steam and water in the cylinder. In reality that moisture has 
furnished the heat which the cylinder walls acquire during 
admission, and it abstracts heat from the walls during the expan- 



HIRN'S ANALYSIS 



205 



sion. The mixture, moreover, is not homogeneous, because the 
moisture on the cylinder walls is likely to be colder than the 
steam, though naturally it cannot be warmer. 

Finally, the indicator-pencil is subject to a friction lag that 
operates to produce the effect shown by Figs. 52 and 53 and is 
liable to exaggerate them. That is to say, the pencil draws a 
horizontal line and tends to remain at the same height after the 
steam-pressure falls. It then lets go and falls sharply some 
little time after the valve has closed at cut-off. Afterwards it 
lags behind and shows a higher pressure than it should. 

Him's Analysis. — Though the methods just illustrated 
give a correct idea of the influence of the walls of the cylinder 
of a steam-engine, our first clear insight into the action of the 
walls is due to Hirn,* who accompanied his exposition by quan- 
titative results from certain engine tests. The statement of his 
method which will be given here is derived from a memoir by 
Dwelshauvers-Dery.t 

Let Fig. 54 represent the cylinder of a steam-engine and the 
diagram of the actual cycle. For sake of simplicity the diagram 
is represented without lead of admission 
or release, but the equations to be deduced 
apply to engines having either or both. 
The points 1,2, 3, and o are the points of 
cut-off, release, compression, and admission. 
The part of the cycle from o to i, that is, 
from admission to cut-off, is represented 
by a\ in like manner, 6, c, and d represent ' yig. 54. 

the parts of the cycle during expansion, 

exhaust, and compression. The numbers will be used as sub- 
scripts to designate the properties of the working fluid under 
the conditions represented by the points indicated, and the 
letters will be used in connection with the operations taking 
place during the several parts of the cycle. Thus at cut-off the 

* Bulletin de la Soc. Ind. de Mulhouse, 1873; Theorie Mechanique de la Chaleur, 
vol. ii, 1876. 

t Revue universelle des Mines, vol. viii, p, 362, 1880. 




1 



^ 



2o6 INFLUENCE OF THE CYLINDER WALLS 

pressure is p^, and the temperature, heat of the liquid, heat of 
vaporization, quality, etc., are represented by /j, q^, r^, x^, etc. 
The external work from cut-off to release is W^, and the heat 
yielded by the walls of the cylinder due to reevaporation is Qi,. 

Suppose that M pounds of steam are admitted to the cylinder 
per stroke, having in the supply-pipe the pressure p and the 
condition x; that is, each pound is x part steam mingled with 
1 — X oi water. The heat brought into the cylinder per stroke, 
reckoned from freezing-point, is 

Q = M {q +xr) (153) 

Should the steam be superheated in the supply-pipe to the 
temperature 4, then 

Q ^ M [r +q + J cdf] . . . . . . (154) 

for which a numerical value can be found in the temperature- 
entropy table. 

Let the heat-equivalent of the intrinsic energy of the entire 
weight of water and steam in the cylinder at any point of the 
cycle be represented by /; then at admission, cut-off, release, 
and compression we have 

A = MA^o +^/o); (155) 

I,= (M ^M,){q, +x,p,)- (156) 

/,= (M +MJ {q, + x,p,)- (157) 

A = M,{q + x^p,); (158) 

in which p is the heat-equivalent of the internal work due to 
vaporization of one pound of steam, and M^ is the weight of 
water and steam caught in the cylinder at compression, calculated 
in a manner to be described hereafter. 

At admission the heat-equivalent of the fluid in the cylinder 
is /q, and the heat supplied by the entering steam up to the point 
of cut-off is Q. Of the sum of these quantities a part, AWa, is 
used in doing external work, and a part remains as intrinsic 
energy at cut-off. The remainder must have been absorbed by 



HIRN'S ANALYSIS 207 

the walls of the cylinder, and will be represented by Qa- Hence 

Qa = Q +1,-1,- AW,. 

From cut-off to release the external work W^, is done, and at 
release the heat-equivalent of the intrinsic energy is I^- Usually 
the walls of the cylinder, during expansion, supply heat to the 
steam and water in the cylinder. To be more explicit, some 
of the water condensed on the cylinder walls during admission 
and up to cut-off is evaporated during expansion. This action 
is so energetic that I^is commonly larger than I,. Since heat 
absorbed by the walls is given a positive sign, the contrary sign 
should be given to heat yielded by them; it is, however, con- 
venient to give a positive sign to all the interchanges of heat in 
the equations, and then in numerical problems a negative sign 
will indicate that heat is yielded during the operation under 
consideration. For expansion, then, 

Q, = A - /, -AW,. 

During the exhaust the external work W^ is done by the engine 
on the steam, the water resulting from the condensation of the 
steam in the condenser carries away the heat Mq^, the cooling 
water carries away the heat G (qj^ — qi), and there remains at 
compression the heat-equivalent of intrinsic energy /j. So that 

Q^ = I^-I^- Mq, - G (q, - q,) + AW,, 

in which ^4 is the heat of the liquid of the condensed steam, and 
G is the weight of cooling water per stroke which has on entering 
the heat of the liquid q^, and on leaving the heat of the Hquid qjt. 

During compression the external work W^ is done by the 
engine on the fluid in the cylinder, and at the end of compression, 
i.e., at admission, the heat-equivalent of the intrinsic energy is I^. 
Hence 

Q^ = I. -h +AWa. ■ 

It should be noted (Fig. 54) that the work Wa is represented 



208 



INFLUENCE OF THE CYLINDER WALLS 



by the area which is bounded by the steam Hne, the ordinates 
through o and i and by the base line. And in Hke manner the 
works Wf,, Wc, and Wa are represented by areas which extend 
to the base line. In working up the analysis from a test the 
line of absolute zero of pressure may be 
drawn under the atmospheric line as in 
Fig. 55, or proper allowance may be 
made after the calculation has been made 
with reference to the atmospheric line. 
For convenience these four equa- 
FiG. 55. tions will be assembled as follows: 




Qa = Q ^1,^-1,- AW,, (159) 

Q, = I,- I,- AW (160) 

Qc = I, - h - Mq, - G (q, - qd + AW, . (161) 
Qa-I. -/o +AW, (162) 

A' consideration of these equations shows that all the quanti- 
ties of the right-hand members can be obtained directly from 
the proper observations of an engine test except the several 
values of I, the heat-equivalents of the intrinsic energies in the 
cylinder. These quantities are represented by equations (155) 
to (158), in which there are five unknown quantities, namely, 

^o» ^v ^v ^v and M,. 

Let the volume of the clearance-space between the valve and 
the piston when it is at the end of its stroke be F^; and let the 
volumes developed by the piston up to cut-off and release be 
Fj and Y ^\ finally, let V ^ represent the corresponding volume 
at compression. The specific volume of one pound of mixed 
water and steam is 



xu 



and the volume of M pounds is 

F = Mv = M {xu + o-). 



HIRN'S ANALYSIS 209 

At the points of admission, cut-off, release, and compression, 

V,= M,(x„u, +0-) (163) 

K„ + F, = (M + M„) {x,u, + <T) (164) 

V, + \\ = {M + M„) {x,u, -,-0-) (165) 

V\ + F, = M, (.T,«3 + "■) (166) 

There is sufficient evidence that the steam in the cylinder 
at compression is nearly if not quite dry, and as there is com- 
paratively little steam present at that time, there cannot be 
much error in assuming 

x^ ^ 1. 

This assumption gives, by equation (i66), 

7 _i_ 7 V + V 

^o--^^xr = ■^-^'^ (^0 + ^)73 . .(167) 

in which 73 is the density or v^eight of one cubic foot of dry 
steam at compression. 

Applying this result to equations (263) to (265) gives 






X,= Tp^-— ....... (168) 



_ F„ + F, f_ 

*= - (M + M„) «, «.■"■■ ^'^°' 

We are now in condition to find the values of I ^^ 7^, /g, and 
73, and consequently can calculate all the interchanges of heat 
by equations (159X to (162). 

Should the value of x in any case appear to be greater than 
unity it indicates that the steam is superheated; this may happen 
for x^^ and then as the weight of steam M^ is relatively small, 
and as the superheating is usually slight, it will be sufficient to 
make x^ equal to unity. It is unlikely to be the case for x^ or x^^ 
even though the steam is strongly superheated in the steam- pipe; 



2IO INFLUENCE OF THE CYLINDER WALLS 

should the computation give a value slightly larger than unity 
the steam may be assumed to be dry without appreciable error, 
and the work may proceed as indicated. If in the use of very 
strongly superheated steam a computed value of x^ is appre- 
ciably larger than unity, we may replace the equation (i66) by 

where v^ is the specific A^olume of superheated steam; conse- 
quently 

F 4- F 
' M ■\-M, 

By aid of the temperature-entropy table we may find (by inter- 
polation if necessary) the corresponding temperature t^ and the 
value of the heat-contents or total heat. The heat-equivalent 
of the intrinsic energy is then equal to this quantity minus Ap^v^. 

In the diagram, Fig. 54, the external work during exhaust is 
all work done by the piston on the fluid, since the release is 
assumed to be at the end of the stroke. If the release occurs 
before the end of the stroke, some of the work, namely, from 
release to the end of the stroke, will be done by the steam on the 
piston, and the remainder, from the end of the stroke back to 
compression, will be done by the piston on the fluid. In such 
case Wc will be the difference between the second and the first 
quantities. If an engine has lead of admission, a similar method 
may be employed; but at that part of the diagram the curves of 
compression and admission can be distinguished with difficulty, 
if at all, and little error can arise from neglecting the lead. 

The several pressures at admission, cut-off, release, and 
compression are determined by the aid of the indicator-diagram, 
and the pressures in the steam-pipe and exhaust-pipe or con- 
denser are determined by gauges. The weight M of steam 
supplied to the cylinder per stroke is best determined by con- 
densing the exhaust-steam in a surface-condenser and collecting 
and weighing it in a tank. If the engine is non-condensing, or 
if it has a jet-condenser, or if for any reason this method cannot 



HIRN'S ANALYSIS 211 

be used, then the feed- water delivered to the boiler may be deter- 
mined instead. The cooling or condensing water, either on 
the way to the condenser or when flowing from it, may be weighed, 
or for engines of large size may be measured by a metre or gauged 
by causing it to flow over a weir or through an orifice. The 
several temperatures t^, ti, and /^ must be taken by proper ther- 
mometers. When a jet-condenser is used, and the condensing 
water mingles with the steam, ^4 is identical with tj^. The quality 
.V of the steam in the supply-pipe must be determined by a steam- 
calorimeter. A boiler with sufficient steam-space will usually 
deliver nearly dry steam; that is, x will be nearly unity. If 
the steam is superheated, its temperature t^ may be taken by a 
thermometer. 

Let the heat lost by radiation, conduction, etc., be Q^; this 
is commonly called the radiation. Let the heat supplied by 
the jacket be Qj. Of the heat supplied to the cylinder per stroke, 
a portion is changed into work, a part is carried away by the 
condensed steam and the cooling or condensing water, and 
the remainder is lost by radiation; therefore 

Qe^Q + Qj--Mq,~G(q,-q,)-A(W,+W,-W,~W^) . (171) 

The heat Qj supplied by a steam-jacket may be calculated 
by the equation 

Qj = m {x'r' ^(t - f) .... (172) 

in which m is the weight of water collected per stroke from the 
jacket; x', r', and ^' are the quality, the heat of vaporization, 
and the heat of the liquid of the steam supplied; and ^" is the 
heat of the liquid when the water is withdrawn. When the 
jacket is supplied from the main steam-pipe, oc^ is the same as 
the quality in that pipe. When suppUed direct from the boiler, 
xf may be assumed to be unity. If the jacket is supplied 
through a reducing-valve, the pressure and quality may be 
determined either before or after passing the valve, since throt- 
tling does not change the amount of heat in the steam. Should 



212 INFLUENCE OF THE CYLINDER WALLS 

the steam applied to the jacket be superheated from any cause, 
we may use the equation 

Qj = m [r' -rq'+ c^ (/./ - /') - ^-] . . . (173) 

in which / and 5' are the heat of vaporization and heat of 
the Hquid of saturated steam at the temperature t\ and Cj is 
the temperature of the superheated steam. 

Equation (171) furnishes a method of calculating the heat 
lost by radiation and conduction; but since Q^ is obtained by 
subtraction and is small compared with the quantities on the 
right-hand side of the equation, the error of this determination 
may be large compared with Q^ itself. The usual way of deter- 
mining (3e for an engine with a jacket is to collect the water 
condensed in the jacket for a known time, an hour for example, 
when the engine is at rest, and then the radiation of heat per 
hour may be calculated. If it be assumed that the rate of radia- 
tion at rest is the same as when the engine is running, the radia- 
tion for any test may be inferred from the time of the test and the 
determined rate. But the engine always loses heat more rapidly 
when running than when at rest, so that this method of 
determining radiation always gives a result which is too 
small. 

If a steam-engine has no jacket it is difficult or impossible 
to determine the rate of radiation. The only available way 
appears to infer the rate from that of some similar engine with 
a jacket. Probably the best way is to get an average value of 
Qe from the application of equation (171) to a series of care- 
fully made tests. 

It is well to apply equation (171) to any test before beginning 
the calculation for Hirn's analysis, as any serious error is likely to 
be revealed, and so time may be saved. 

When the radiation Q^, is known from a direct determination 
of the rate of radiation, we may apply Hirn's analysis to a test 
on an engine even though the quantities depending on the con- 
denser have not been obtained. For from equation (171) 



HIRN'S ANALYSIS 213 

-Mq, -G{q,~ qi) = Q, -Q-Qj i- A(Wa + W," W ,- Wa), 
and consequently 

g. = /, - 7. - (? - Q:, + (2e + ^4 iyv,. -^W,-W,) . . (174) 

Thus it is possible to apply the analysis to a non-con- 
densing engine or to the high-pressure cylinder of a compound 
engine. 

It is apparent that the heat Qcj thrown out from the walls 
of the cylinder during exhaust, passes without compensation 
to the condenser, and is a direct loss. Frequently it is the 
largest source of loss, and for this reason Hirn proposed to make 
it a test of the performance and perfection of the engine; but 
such a use of this quantity is not justifiable, and is likely to 
lead to confusion. 

The heat Q^ that is restored during expansion is supplied at 
a varying and lower temperature than that of the source of heat, 
namely, the boiler, and, though not absolutely wasted, is used 
at a disadvantage. It has been suggested that an early com- 
pression, as found in engines with high rotative speed, warms 
up the cylinder and so checks initial condensation, thereby 
reducing Qa and finally Q^ also. Such a storing of heat during 
compression and restoring during expansion is considered to 
act like the regenerator of a hot-air engine, and to make the 
efficiency of the actual cycle approach the efficiency of the ideal 
cycle more nearly than would be the case without compression. 
It does not, however, appear that engines of that type have 
exceeded, if they have equalled, the performance of slow-speed 
engines with small clearance and little compression. 

Application. — In order to show the details of the method of 
applying Hirn's analysis the complete calculation for a test 
made on a small Corliss engine in the laboratory of the Massa- 
chusetts Institute of Technology will be given. Its usefulness is 
mainly as a guide to any one who may wish to apply the method 
for the first time. 



214 INFLUENCE OF THE CYLINDER WALLS 

Diameter of the cylinder 8 inches. 

Stroke of the piston 2 feet. 

Piston displacement: crank end 0.6791 cu. ft. 

head end 0.7016 " " 

Clearance, per cent of piston displacement : 

crank end •3-75 

head end 5.42 

Boiler-pressure by gauge 77.4 pounds. 

Barometer 14.8 " 

Condition of steam, two per cent of moisture. 
Events of the stroke: 

Cut-off: crank end 0.306 of stroke. 

head end 0.320 " 

Release at end of stroke. 

Compression: crank end .... 0.013 o^ stroke. 

head end 0.0391 " 

Duration of the test, one hour. 

Total number of revolutions 3692 

Weight of steam used 548 pounds. 

Weight of condensing water used . . . 14,568 " 

Temperatures : 

Condensed steam t^= 141°.! F. 

Condensing water: cold U = $2°. 9 F. 

warm 4 =- 88^.3 F. 

* ABSOLUTE PRESSURES, FROM INDICATOR-DIAGRAMS, AND 
CORRESPONDING PROPERTIES OF SATURATED STEAM. 





Crank End. 


Head End. 




/ 


(7 


p 


u 


/ 


1 


p 


M 


Cut-off . . . 
Release . . . 
Compression . 
Admission 


83.6 
29.2 
14.8 
21.8 


284.6 
217.8 
181. 1 
201.5 


813.0 
864.8 
893.2 
877.4 


5.190 
13.924 
26.464 
18.344 


83-3 

31-9 
14.8 
29.8 


284.4 
222.9 
181. 1 
219.0 


813.2 
860.8 
893.2 
863.9 


5.207 
I 2 . 804 
26.464 
13.664 



* These values are taken from the first edition of the Tables of Properties of 
Saturated Steam. 



APPLICATION 



215 



MEAN PRESSURES, -\ND HEAT-EQUIVALENTS OF EXTERNAL 

WORKS. 





Ckank End. 


Head End. 




Mean Pressures. 


Equivalents of 
Work. 


Mean Pressures. 


Equivalents of 
Work. 


Admission 
Expansion .... 

Exhaust 

Compression . . . 


87.7 

44-5 
14.8 

18.3 


3-369 
3-877 
1.836 

0.0290 


89-3 

14.8 

21.8 


3-7II 

4-159 
1.847 

0. I 104 



VOLUMES, CUBIC FEET. 





Crank End. 


Head End. 


At cut-oflF, ■^'o + ^'1 

At release, Vq+ V^ 

At compression, Vq+V^ 

At admission, V^ 


0.2333 
0.7046 
0.0343 
0.02550 


0.2626 
0.7396 
0.0655 
0.03806 





At the boiler-pressure, 92.1 pounds absolute, we have 

r = 888.4, q = 291.7. 

The steam used per stroke is 
548 



M 



3692 



= 0.0742 pound. 



The steam caught in the clearance space at compression, on 
the assumption that the steam is then dry and saturated, is 
obtained by multiplying the mean volume at that point by the 
weight of one cubic foot of steam at the pressure at compression, 
which is 0.03781 of a pound. 

,, 0.0^43 + o.o6s^ „ - 

.'. Mq = — "^-^ ^^ X 0.03781 = 0.0019 of ^ pound; 

M -f- Mq = 0.0742 H- 0.0019 ^ 0.0761 pound. 
The condensing water used per stroke is 



G = 



14568 
2 X 3692 



= I-973- 



2i6 INFLUENCE OF THE CYLINDER WALLS 

Q = M (xr + q) = 0.0742(0.98 X 888.3 + 291.8) = 86.243; 
i (0.02550 + 0.03806) 1 



*'"" 0.0019X^(18.344+13.664) 62.4X^(18.344+13.664) 
= 1.043. 

This indicates that the steam is superheated at admission. 
Such may be the case, or the appearance may be due to an 
error in the assumption of dry steam at compression, or to errors 
of observation. It is convenient to assume ^'0 = i. 

,. v. + v. 



X 



i (0-2333 + 0.2626) 



' 0.0761 X i (5.190 + 5.207) 62.4 X i(5-i9o + 5-207) 
= 0.6236. 



V -\- V 



(M + MJ u^ u, ' 
-I (0.7046 + 0.7396) 



0.0761X^(13.924+12.804) 62.4x4(13.924+12.804) 
= 0.7088. 

.'. I(y= i X 0.0019 [201.5 + 219.0 + i.oo (877.4 + 863.9)] 
= 2.054. 

I,= (M +M,)iq,+x,p^); 

•'- ^1 = 2 X 0.0761 [284.6 + 284.4 + 0.6236 (813.0 +813.2)] 
= 60.238. 
/, = {M +MJ {q, +x^,); 
,', I^ = i- X 0.0761 [217.8+222.0 + 0.7088 (864.8 + 861.8)] 
= 63.311. 
h = M,(q, +x^^); 
.'. I3 = 0.0019 (181. 1 + 893.2) = 2.041. 



APPLICATION 217 

Qa = Q +h- ^ -AW,; 
.-. Qa = 86.243 + 2.054 - 60.238 - 1 (3.369+3-711) = 24.519. 

.-. Q, = 60.238 - 63.311 - J (3.877 + 4.159) = - 7.091- 

Qr = I,- Is- Mq, - G (q, - qd + AW,; 
.-. Q, - 63.311 - 2.041 - 0.0742 X 109.3 

- 1.973 (56.35 - 21.01) + i (1.836 + 1.847) 
= - 14-721. 
Q, = I,-h +AWa; 
.-. Qd = 2.041 - 2.054 + J (0.0299 + 0.1104) = 0.157. 

Qe = Qa +Qo +Qc +Q4- 2.764. 

Also, equation (171) for this case gives 
Qe-^Q- Mq, -G{q,- q,) - AW 

= 86.243— 8. no — 69.723 — (3.540+4.018 — 1.841 — 0.070) 
= 86.243—8.110 — 69.723 — 5.647 = 2.764. 

It is to be remembered that the heat lost by radiation and 
conduction per stroke, when estimated in this manner, is affected 
by the accumulated errors of observation and computation, 
which may be a large part of the total value of Q^. 

Dropping superfluous significant figures, we have in b.t.u. 

Q = 86.2, Qa = 24.5, Q.b= - 7-1, 

Qc= - 14.7^ Qd = .06, Q, = 2.8. 

Noting that 5.647 are the b.t.u. changed into work per stroke 
and 3692 the total revolutions the horse-power of the engine is 

778 X 5.6 4 7 X 3692 X 2 _ ^ jjp^, 

60 X 33000 

and the steam per horse-power per hour is 
-^^— - 33-5 pounds. 



16.35 
For data and results of this test and others see Table IV. 



2l8 



INFLUENCE OF THE CYLINDER WALLS 



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gUUnp SIJBM (5) 

"Aq papBA 


vd dv^^d>4 


•aoiSHKdxa 

SUUa'p SIIBA\ Q, 


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j 


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Ov PI PI t^ lo 1 


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JO spunod Oi 


2vS5_2? 

to PI po 4vd 

Tf ui lOOOO 

1 


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"o 

f 






00- •t OvO o i 

d d d d d 




PI «0 PI Ov Ov 

d d d d d 


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fo ooo Tj- 1^ 

t~. PIO Tt 'i- 
r^oOOOOOOO 

M M M M M 




r^ PI Tt OO 
M p< lo ro CO 
00 00 00 00 00 




w 


oJ^v^^s; 

M r^ioOvM 
ro K^ tOPTI 4 




lo PI »^ r» 

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M PI c« loOO 

f^ PO PO to PO 


o 




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»^00 PO M M 

Ov fOO PI t^ 

d M M pi f^ 


u 


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M M M PI fO 


it 
li 

■il 


il 


t4 


r-O ■*© Ov 
t^4ro4po 


d 


PI roOviOPO 

PI M d M M 


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22222 


c3 


88888 


to 

o 

u 


p4 


O PI O «oO 




O PI O »o>0 




•jaquinisi 




1 ^««^« 



SUPERHEATED STEAM 219 

Effect of Varying Cut-off. — An inspection of the interchanges 
of heat shows that the values of Qa, the heat absorbed by the 
walls during admission, increase regularly as the cut-off is 
lengthened, and that the heat returned during expansion decreases 
at the same time, so that there is a considerable increase in the 
value of the heat Qc which is rejected during exhaust. Never- 
theless there is a large gain in economy from restricting the 
cut-off so that it shall not come earlier than one- third stroke. 
Unfortunately tests on this engine with longer cut-off than one- 
third stroke have not been made, and consequently the poorer 
economy for long cut-off cannot be shown for this engine as for 
the engine of the Michigan. 

Hallauer*s Tests. — In Table V are given the results of a 
number of tests made by Hallauer on two engines, one built by 
Hirn having four flat gridiron valves, and the other a Corliss 
engine having a steam-jacket. Two tests were made on the 
former with saturated steam and six with superheated steam. 
Three tests were made on the latter with saturated steam and 
with steam supplied to the jackets. These tests have a historic 
interest, for though not the first to which Hirn's analysis was 
applied, they are the most widely known, and brought about the 
acceptance of his method. They have also a great intrinsic 
value, as they exhibit the action of two different methods of 
ameliorating the effect of the action of the cylinder walls, namely, 
by the use of superheated steam and of the steam-jacket. In all 
these tests there was little compression, and Qa, the interchange 
of heat during compression, is ignored. 

Superheated Steam. — Steam from a boiler is usually slightly 
moist, Xj the quality, being commonly 0.98 or 0.99. Some boilers, 
such as vertical boilers with tubes through the steam space, give 
steam which is somewhat superheated, that is, the steam has a 
temperature higher than that of saturated steam at the boiler- 
pressure. Strongly superheated steam is commonly obtained by 
passing moist steam from a boiler through a coil of pipe, or a 
system of piping, which is exposed to hot gases beyond the 
boiler. 



220 



INFLUENCE OF THE CYLINDER WALLS 



< 



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z 



SUPERHEATED STEAM 221 

- Superheated steam may yield a considerable amount of heat 
before it begins to condense; consequently where superheated 
steam is used in an engine a portion of the heat absorbed by the 
walls during admission is supplied by the superheat of the steam 
and less condensation of steam occurs. This is very evident in 
Dixwell's tests given by Table XXV, on page 271, where the 
water in the cylinder at cut-off is reduced from 52.2 per cent to 
27.4 per cent, when the cut-off is two-tenths of the stroke, by 
the use of superheated steam; with longer cut-off the effect is 
even greater. This reduction of condensation is accompanied 
by a very marked gain in economy. 

The way in which superheated steam diminishes the action 
of the cylinder walls and improves the economy of the engine is 
made clear by Hallauer's tests in Table V. A comparison of 
tests I and 3, having six expansions, shows that the heat Q„ 
absorbed during admission is reduced from 28.3 to 22.4 per cent 
of the total heat supplied, and that the exhaust waste is corre- 
spondingly reduced from 21.6 to 12.5 per cent. A similar 
comparison of tests 2 and 5, having nearly four expansions, 
shows even more reduction of the action of the cylinder walls. 
The effect on the restoration of heat Qi, during expansion appears 
to be contradictory: in one case there is more and in the other 
case less. It does not appear profitable to speculate on the 
meaning of this discrepancy, as it may be in part due to errors 
and is certainly affected by the unequal degree of superheating 
in tests 3 and 5. It may be noted that the actual value of Qc in 
calories is nearly the same for tests i and 2, there being a small 
apparent increase with the increase of cut-off, which is, however, 
less than the probable error of the tests. The exhaust waste Q^ 
is much more irregular for tests 3 to 7 for superheated steam. 
The increase from 81 to 87 b.t.u. from test 6 to test 7 may 
properly be attributed to a less degree of superheating; the 
increase from 66 to 81 b.t.u. for tests 5 and 6 is due to longer 
cut-off and less superheating; finally, the steady reduction from 
75 to 66 B.T.U. for the three tests 3, 4, and 5 is probably due to 
the rise of temperature of the superheated steam, which more 



222 INFLUENCE OF THE CYLINDER WALLS 

than compensates for the effect of lengthening the cut-off. 
Finally in test 8 the exhaust waste is practically reduced to 
zero by the use of strongly superheated steam in a non-con- 
densing engine; this shows clearly that the exhaust waste Qc by 
itself is no criterion of the value of a certain method of using 
steam. 

Steam-jackets. — If the walls of the cylinder of a steam- 
engine are made double, and if the space between the walls is 
filled with steam, the cylinder is said to be steam- jacketed. 
Both barrel and heads may be jacketed, or the barrel only may 
have a jacket; less frequently the heads only are jacketed. The 
principal effect of a steam-jacket is to supply heat during the 
vaporization of any water which may be condensed on the 
cylinder walls. The consequence is that more heat is returned 
to the steam during expansion and the walls are hotter at the 
end of exhaust than would be the case for an unjacketed engine. 
This is evident from a comparison of tests i and ii in Table V. 
In test I only a small part of the heat absorbed during admission 
is returned during expansion, and by far the larger part is wasted 
during exhaust. In test ii the heat returned during expansion 
is equal to two-thirds that absorbed during admission, though a 
part of this heat of course comes from the jacket. About half 
as much is wasted during exhaust as is absorbed during admission. 
The condensation of steam is thus reduced indirectly; that is, 
the chilling of the cylinder during expansion, and especially 
during exhaust, is in part prevented by the jacket, and conse- 
quently there is less initial condensation and less exhaust waste, 
and in general a gain in economy. The heat supplied during 
expansion, though it does some work, is first subjected to a 
loss of temperature in passing from the steam in the jacket to 
the cooler water on the walls of the cylinder, and such a non- 
reversible process is necessarily accompanied by a loss of effi- 
ciency. On the other hand, the heat supplied by a jacket during 
exhaust passes with the steam directly into the exhaust-pipe. 
It appears, then, that the direct effect of a steam-jacket is to 
waste heat; the indirect effect (drying and warming the cylinder) 



APPLICATION TO MULTIPLE-EXPANSION ENGINES 223 

reduces the initial condensation and the exhaust waste and often 
gives a notable gain in economy. 

Application to Multiple-expansion Engines. — The application 
of Hirn's analysis to the high- pressure cylinder of a compound* or 
multiple-expansion engine may be made by using equations 
(159), (160), and (162) for calculating Qa, Qb, and Qa, while 
equation (174) may be used to find Qc. 

A similar set of equations may be written for the next cylinder, 
whether it be the low-pressure cylinder of a compound engine 
or the intermediate cylinder of a triple engine, provided we can 
determine the value of Q', the heat supplied to that cylinder. 
But of the heat supplied to the high-pressure cylinder a part 
is changed into work, a part is radiated, and a part is rejected 
in the exhaust waste. The heat rejected is represented by 

Q +Qj-AW -Q, (175) 

where Q is the heat supplied by the steam entering the cylinder, 
Qj is the heat supplied by the jacket, ^W is the heat-equivalent 
of the work done in the cylinder, and Qe is the heat radiated. 
Suppose the steam from the high-pressure cylinder passes to an 
intermediate receiver, which by means of a tubular reheater or 
by other means supplies the heat Q,., while there is an external 
radiation Qre- The heat supplied to the next cylinder is con- 
sequently 

Q' = Q i^Qj- AW -Q,+ Qr -Qre • • (176) 

In a like manner we may find the heat Q" supplied to the 
next cylinder ; for example, to the low-pressure cylinder of a 
triple engine. 

It is clear that such an application of Hirn's analysis can be 
made only when the several steam-jackets on the high- and the 
low-pressure cylinders, and the reheater of the receiver, etc., 
can be drained separately, so that the heat supplied to each 
may be determined individually. 

Table VI gives applications of Hirn's analysis to four tests 
on the experimental triple-expansion engine in the laboratory 
of the Massachusetts Institute of Technology. 



224 INFLUENCE OF THE CYLINDER WALLS 

It will be noted that the steam in the cylinders becomes drier 
in its course through the engine, under the influence of thorough 
steam-jacketing with steam at boiler-pressure, and is practically 
dry at release in the low-pressure cylinder. All of the tests 
show superheating in the low-pressure cyhnder, which is of 
course possible, for the steam in the jackets is at full boiler^ 
pressure while the steam in the cylinder is below atmospheric 
pressure. The superheating was small in all cases — not more 
than would be accounted for by the errors of the tests. The 
exhaust waste Q^' from the low-pressure cylinder in the triple- 
expansion tests is very small in all cases — less than two per cent 
of the heat supplied to the cylinders. The apparent absurdity of 
a positive value for Q^' in two of the tests (indicating an absorp- 
tion of heat by the cylinder walls during exhaust) may properly 
be attributed to the unavoidable errors of the test. 

In the fourth test, when the engine was developing 120.3 
horse-power, there were 1305 pounds of steam supplied to the 
cylinders in an hour, and 345 pounds to the steam-jackets; so 
that the steam per horse-power per hour passing through the 
cylinders was 

1305 -^ 120.3 =^ 10.86 pounds, 

while the condensation in the jackets was 

345 ^ 120.3 "^ 2.87 pounds. 

So that, as shown on page 145, the b.t.u. per horse-power per 
minute supplied to the cylinders by the entering steam was 
191. 1, while the jackets supplied 40.6 b.t.u., making in all 
231.7 B.T.U. per horse-power per minute for the heat-consumption 
of the engine. In the same connection it was shown that the 
thermal efficiency of the engine for this test was 0.183, while 
the efficiency for incomplete expansion in a non-conducting 
cylinder corresponding to the conditions of the test was 0.222; 
so that the engine was running with 0.824 of the possible efficiency. 
In light of this satisfactory conclusion some facts with regard to 
the test are interesting. 



APPLICATION OF HIRN'S ANALYSIS 



225 



Table VI. 

APPLICATION OF HIRN'S ANALYSIS TO THE EXPERIMENTAL 
ENGINE IN THE LABORATORY OF THE MASSACHUSETTS 
INSTITUTE OF TECHNOLOGY. 

TRIPLE-EXPANSIOX; CYLINDER DIAMETERS, 9, 1 6, AND 24 INCHES ; STROKE, 30 

INCHES. 

Trans. Am. Soc. Mech. Engrs., vol. xii, p. 740. 



Duration of test, minutes 

Total number of revolutions .... 

Revolutions per minute 

Steam-consumption during test, lbs. : 
Passing through cylinders .... 
Condensation in h.p. jacket , . . 

in first receiver-jacket 

in inter, jacket 

in second receiver-jacket .... 

in l.p. jacket 

Total . 

Condensing water for test, lbs. . . . 

Priming, by calorimeter 

Temperatures, Fahrenheit : 

Condensed steam 

Condensing-water, cold 

Condensing-water, hot 

Pressure of the atmosphere, by the 

barometer, lbs. per sq. in 

Boiler pressure, lbs. per sq. in. abso- 
lute 

Vacuum in condenser, inches of mer- 
cury 

Events of the stroke: 

High-pressure cylinder — 

Cut-off, crank end 

head end 

Release, both ends 

Compression, crank end . . . 

head end 

Intermediate cylinder — 

Cut-ofT, both ends ..... 

Release, both ends 

Compression, crank end . . . 

head end 

Low-pressure cylinder — 

Cut-off, crank end 

head end 

Release, both ends 



60 
5299 



1 193 

57 
61 

85 
53 



1538 

:2847 

0.013 

95-4 
41.9 
96. 1 

14.8 

155-3 
25.0 



o. 192 
0.215 
1 .00 

0.05 
0.0:; 



60 

5228 

87- 

1157 
50 
64 

92 
50 
76 



1489 



22186 
0.012 

92. 1 
42.1 
96.6 

14.8 

155-5 
25.1 



0.194 
0.205 
1. 00 

0.05 
0.05 

0.29 
1. 00 
0.03 
0.04 



0.38 

0-39 
1. 00 



III. 



IV 



60 
5173 

86. 



1234 
29 
69 

97 

52 
90 



^571 

20244 

o.oii 

102.4 

43-0 
106.3 

14.7 

156.9 

24.1 



0.245 
0.271 
1. 00 
0.04 
0.05 

o. 29 
1 .00 

0.03 
p. 04 



0.38 
0-39 

1 .00 



60 
5148 
85.8 

1305 
30 

72 

105 

5^ 

87 



1650 

20252 

0.012 

105-3 

42.8 

109.6 

14.7 

157-7 

23-9 



0.183 

0-305 
1 .00 
0.04 
0.05 

0.29 
1 .00 
0.03 
0.04 

0.38 
0.39 



2 26 



INFLUENCE OF THE CYLINDER WALLS 



Table VI — Continued. 



Absolute pressures in the cylinder, 
pounds per sq. in. : 
High-pressure cylinder — 

Cut-off, crank end 

head end 

Release, crank end 

head end 

Compression, crank end .... 

head end 

Admission, crank end 

head end 

Intermediate cylinder — 

Cut-off, crank end 

head end 

Release, crank end 

head end 

Compression, crank end .... 

head end 

Admission, crank end 

head end 

Low-pressure cylinder — 

Cut-off, crank end 

head end 

Release, crank end 

head end 

Compression and admission — 

crank end , . 

head end 

Heat-equivalents of external work, 
B.T.U., from a reason indicator- 
diagram to line of absolute vacuum : 
High-pressure cylinder — 
During admission, 

A Wd, crank end ...... 

head end 

During expansion, 

.41^6, crank end 

head end 

During exhaust, 

ylW^e, crank end 

head end 

T3uring compression, 

^l^d, crank end ...... 

head end 

Intermediate cylinder — 
During admission, 

A Wa, crank end 

head end ... 

During expansion, 

A Wh , crank end 

head end 



145-9 
143.2 

41.3 
41-5 
43-7 
48.7 

64-5 
75-3 



5-71 
6.6j 



10.65 
10.81 



7-73 
8.08 



0.48 
0.62 



7-58 
7-43 

9-54 
9. 22 



145 

143 

41 

40 

45 
47 
68 

74 

37 
35 

T4 

13 
17 
18 
20 
22 

12 
12 

5 
5 

3 
4 



5-78 
6-37 

10.76 

T I . 04 

7.89 
8.15 

o. 60 

0.64 



9-54 
9.3T 



III. 



138.8 

140.3 

44-7 

45-7 
48.5 
54-5 
72.2 



38. 
39- 
14- 
14. 
18. 
20. 
22. 
24. 



12.4 

13-1 

5-1 

5-9 



4.1 
4.6 



7.00 
8.42 

10.40 
11.22 

8.44 
9.04 

0.49 
0-73 



7.98 
8.46 

9.91 
10.37 



IV. 



138-3 
140,6 

48.4 
49.8 
53-2 
62.0 
81.2 
97.8 

40.9 
42.6 
16.0 
16.0 
19.0 
22.4 
23.1 
26.7 

13.2 

14.0 

5-7 

6.4 

4.2 

4.7 



8.19 
9-5° 

10.25 
11.09 

9.02 
9.66 

0.50 
0.81 



8.64 
9. 10 

10.64 

TI . 14 



APPLICATION OF HIRN'S ANALYSIS 

Table VI — Continued. 



227 





I. 


II. 


m. 


IV. 


Intermediate cylinder — 










During exhaust, 










^P^/, crank end 


9.27 


9-47 


9.64 


10.54 


head end 


9.27 


9-47 


10.18 


10.84 


During' compression, 










^^/, crank end 


0-39 


0.43 


0.57 


0.46 


head end 


0.60 


0. 70 


0.78 


0.84 


Ix)w-pressure cylinder — 










During admission, 










^HV, crank end 


l-IS 


7-95 


8.33 


8.97 


head end 


7 


99 


8.19 


8.66 


9-39 


During expansion, 












^IPFft'', crank end 


6 


83 


7.10 


6.86 


7-45 


head end 


6 


87 


7.12 


7-34 


.7.87 


During exhaust, 












^Pi^/', crank end 


5 


08 


5.08 


4.62 


5-09 


head end 


5 


08 


S-i6 


4.81 


5.00 


During compression, 












^PF/', crank end 





00 


0.00 


0,00 


0.00 


head end 





00 


0.00 


0.00 


0.00 


< Quality of the steam in the cy Under. 










At admission and at compression 










the steam was assumed to be dry 










and saturated: 










High-pressure cylinder — 










At cut-off x^ . 


0.785 


0.784 


0.848 


0-875 


At release x^ . 


0.899 


0.903 


0.920 


0.931 


Intermediate cyUnder — 










At cut-off a;/ . 


0.899 


0.912 


0.906 


0.908 


At release X2' . 


0.994 


* * * 


={= * * 


* * * 


Low-pressure cylinder — 










At cut-off Xx" . 


0.978 


* * * 


0.970 


0.974 


At release x/' . 


:!< * * 


* * * 


* * * 


* * * 


Interchanges of heat between the 










steam and the walls of the cylin- 










ders, in B. T. u. Quantities 










affected by the positive sign are 










absorbed by the cylinder walls; 










quantities affected by the negative 










sign are yielded by the walls: . . 










High-pressure cylinder — 










Brought in by steam . Q . . . 


132.93 


130.77 


141. II 


149.84 


During admission . . . Qd 


23.54 


23-43 


17.49 


14.93 


During expansion . . . Qb . . 


-18.69 


-19.28 


-15-33 


— 14.03 


During exhaust . . . . Qc . . 


- 8.36 


- 7.22 


- 3-50 


- 2.38 


During compression . . Qd . . 


0.45 


0.51 


0.49 


0.52 


Supplied by jacket ■ . Qj . . 


4.56 


4.08 


2.39 


2.50 


Lost by radiation . . . Qc . . 


T.5O 


1.52 


1.54 


I -54 


First intermediate receiver — 










Supplied by jacket . . Qr ■ . 


4.92 


5.20 


5-67 


5-95 


Lost by radiation . . . Qrc . . 


0.58 


0.58 


0-59 


0.59 



Superheated. 



228 



INFLUENCE OF THE CYLINDER WALLS 



Table VI — Continued. 





I. 


II. 


III. 


IV. 


Intermediate cylinder — 










Brought in by steam . Q' . . 


131.89 


129. 61 


^37-87 


146.64 


During admission . . . Qa' . . 


13.62 


11.74 


11-33 


ir-75 


During expansion . . . Qb . . 


-18.65 


-18.84 


-20.30 


-21.88 


During exhaust .... Q,/ . . 


0.22 


1-57 


2.88 


3-41 


During compression . . Qd . ■ 


0.44 


0.51 


0.62 


0-59 


SuppHed by jacket . . Q/ . . 


6.82 


7-50 


7-97 


8.64 


Lost by radiation . . . Q/ ■ ■ 


2.45 


2.48 


2.50 


2.51 


Second intermediate receiver - 










Supplied by jacket . . Q/ . . 


4.20 


4.04 


4.27 


4.22 


Lost by radiation . . . Qre' ■ ■ 


1.20 


1.22 


1.23 


1.24 


Low-pressure cyHnder — 










Brought in by steam . Q" . . 


132.14 


130-50 


T38.61 


147-33 


During admission . . . Q/' ■ ■ 


5.85 


3-05 


5-57 


5-29 


During expansion . . . Qb" ■ . 


- 9-51 


- 7-09 


- 8.65 


-10.13 


During exhaust .... Q/' ■ ■ 


2.53 


2.23 


- 1-44 


— 0. II 


During compression . . Qd" ■ . 


0.00 


0.00 


0.00 


0.00 


Supplied by jacket . . Q/' . . 


7-. 08 


6. 20 


7.41 


7-14 


Lost by radiation . . . Q/' . . 


4.34 


4.40 


4.45 


4-47 


Total loss by radiation — 










By preliminary tests . . ^Qe ■ . 


10.07 


10.20 


10.31 


10-35 


By equation (171) 


11.68 


TO. IQ 


8.75 


8.07 


Power and economy: 










Heat-equivalents of works per 










stroke — 










H.P. cylinder , . . . AW . . 


8.44 


8.34 


9.17 


9.52 


Interm. cyHnder. . . . AW . 


7.12 


6-95 


7-77 


8.42 


L. P. cylinder . . . . AW" . 


9.64 


10.06 


10.87 


11.79 


Totals 


25.20 
27.58 


25-35 
27.02 


27.81 

27.71 


29-73 
28.45 


Total heat furnished by jackets . . 


Distribution of work — 










High-pressure cyHnder 


1. 00 


1. 00 


1. 00 


1. 00 


Intermediate cylinder 


0.84 


0.83 


0.85 


0.88 


Low-pressure cyHnder ..... 


1. 14 


1. 21 


1. 19 


1.24 


Horse-power 


104.9 
14.65 


104. 2 


113. 1 
13.90 


120.3 
13-73 


Steam per H.P. per hour 


14- 3' 


B.T.U. per H.P. per minute . . . 


247 


241 


236 


232 



It will be noted that for test IV 149.84 b.t.u. per stroke are 
brought in by the steam suppHed to the high-pressure cylinder 
and that 28.45 b.t.u. per stroke are supplied by the steam-jackets; 
and that, further, 29.73 b.t.u. are changed into work while 10.35 
are radiated. Thus it appears that the jackets furnished almost 
as much heat as was required to do all the work developed. Of 
the heat furnished by the jackets something more than a third 



QUALITY OF STEAM AT COMPRESSION 229 

was radiated; the other two-thirds may fairly be considered 
to have been changed into work, since the exhaust w^aste of the 
low-pressure cylinder was practically zero. 

Quality of Steam at Compression. — In all the work of this 
chapter the steam in the cylinder at compression has been con- 
sidered to be dry and saturated, and it has been asserted that 
little if any error can arise from this assumption. It is clear 
that some justification for such an assumption is needed, for a 
relatively large weight of water in the cylinder would occupy 
a small volume and might well be found adhering to the cylinder 
walls in the form of a film or in drops; such a weight of water 
would entirely change our calculations of the interchanges of 
heat. The only valid objection to Hirn's analysis is directed 
against the assumption of dry steam at compression. Indeed, 
when the analysis w^as first presented some critics asserted that 
the assumption of a proper amount of water in the cylinder is 
all that is required to reduce the calculated interchanges of heat 
to zero. It is not difficult to refute such an assertion from 
almost any set of analyses, but unfortunately such a refutation 
cannot be made to show conclusively that there is little or no 
water in the cylinder at compression; in every case it will show 
only that there must be a considerable interchange of heat. 

For the several tests on the Hirn engine given in Table V, 
Hallauer determined the amount of moisture in the steam in the 
exhaust-pipe, and found it to vary from 3 to 10 per cent. Professor 
Carpenter * says that the steam exhausted from the high-pressure 
cylinder of a compound engine showed 12 to 14 per cent of 
moisture. Numerous tests made in the laboratory of the 
Massachusetts Institute of Technology show there is never a 
large percentage of water in exhaust-steam. Finally, such a 
conclusion is evident from ordinary observation. Starting from 
this fact and assuming that the steam in the cylinder at com- 
pression is at least as dry as the steam in the exhaust-pipe, we 
are easily led to the conclusion that our assumption of dry steam 
is proper. Professor Carpenter reports also that a calorimeter 

' * Trans. Am. Soc. Mech. Engrs., vol. xii, p. 811. 



230 INFLUENCE OF THE CYLINDER WALLS 

test of steam drawn from the cylinder during compression 
showed little or no moisture. Nevertheless, there would still 
remain some doubt whether the assumption of dry steam at 
compression is really justified, were we not so fortunate as to- 
have direct experimental knowledge of the fluctuations of tem- 
perature in the cylinder walls. 

Dr. Hall's Investigations. — For the purpose of studying 
the temperatures of the cylinder walls Dr. E. H. Hall used a 
thermo-electric couple, represented by Fig. 56. / is a casi- 
^vwwsAi vi/ iron plug about three-quar- 



HaJvwwnM/ 



Fig. 56. 



ters of an inch in diameter, 
which could be screwed into 
the hole provided for attach- 
ing an indicator-cock to the 
cylinder of a steam-engine. The inner end of the plug 
carried a thin cast-iron disk, which was assumed to act as 
a part of the cylinder wall when the plug was in place. To 
study the temperature of the outside surface of the disk a nickel 
rod N was soldered to it, making a thermo-electric couple. 
Wires from / and N led to another couple made by soldering 
together cast-iron and nickel, and this second couple was placed 
in a bath of paraffine which could be maintained at any desired 
temperature. In the electric circuit formed by the wires joining 
the two thermo-electric couples there was placed a galvanometer 
and a circuit-breaker. The circuit-breaker was closed by a 
cam on the crank-shaft, which could be set to act at any point 
of the revolution. If the temperature of the outside of the disk 
5* differed from the temperature of the paraffine bath at the instant 
when contact was made by the earn, a current passed through 
the wires and was indicated by the galvanometer. By properly 
regulating the temperature of the bath, the current could be 
reduced and made to cease, and then a thermometer in the bath 
gave the temperature at the surface of the disk for the instant 
when the cam closed the electric circuit. Two points in the 
steam-cycle were chosen for investigation, one immediately 
after cut-off and the other immediately after compression, since 



CALLENDAR AND NICOLSON'S INVESTIGATIONS 231 

they gave the means of investigating the heat absorbed during 
compression and admission of steam, and the heat given up 
during expansion and exhaust. 

Three different disks were used : the first one half a miUimetre 
thick, the second one miUimetre thick, and a third two miUi- 
metres thick. From the fluctuations of temperature at these 
distances from the inside surface of the w^all some idea could be 
obtained concerning the variations of temperature at the inner 
surface of the cylinder, and also how far the heating and cooling 
of the walls extended. 

The account given here is intended only to show^ the general 
idea of the method, and does not adequately indicate the labor 
difficulties of the investigation which involved many secondarv 
investigations, such as the determination of the conductivity of 
nickel. Having shown conclusively that there is an energetic 
action of the walls of the cylinder. Dr. Hall was unable to continue 
his investigations. 

Callendar and Nicolson's Investigations. — A very refined 
and complete investigation of the temperature of the cylinder 
walls and also of the steam in the cylinder was made by 
Callendar and Nicolson * in 1895 at the McGill University, 
by the thermo-electric method. 

The wall temperatures were determined by a thermo-electric 
couple of which the cylinder itself was one element and a WTought- 
iron wire was the other element. To make such a couple, the 
cylinder wall was drilled nearly through, and the wire was 
soldered to the bottom of the hole. Eight such couples were 
established in the cylinder-head, the thickness of the unbroken 
wall varying from o.oi of an inch to 0.64 of an inch. Four pairs 
of couples were established along the cylinder-barrel, one near 
the head, and the others at 4 inches, 6 inches, and 12 inches 
from the head. One of each pair of wall couples was bored to 
within 0.04 of an inch, and the other to 0.5 of an inch of the 
inside surface of the cylinder. Other couples were established 
along the side of the cylinder to study the flow of heat from the 

* Proceedings of the Inst. Civ. Engrs., vol. cxxxii. 



232 



INFLUENCE OF THE CYLINDER WALLS 



head toward the crank end. The temperature of the steam 
near the cyhnder-head was measured by a platinum thermometer 
capable of indicating correctly rapid fluctuations of temperature. 

The engine used for the investigations was a high-speed 
engine, with a balanced slide-valve controlled by a fly-wheel 
governor. During the investigations the cut-off was set at a 
iixed point (about one-fifth stroke), and the speed was controlled 
vxtcrnally. By the addition of a sufficient amount of lap to 
prevent the valve from taking steam at the crank end the engine 
was made single-acting. The normal speed of the engine was 
250 revolutions per minute, but during the investigations the speed 
was from 40 to 90 revolutions per minute. The diameter of the 
cylinder was 10.5 inches and the stroke of the piston was 12 
inches. The clearance was ten per cent of the piston displacement. 

From the indicator-diagrams an analysis, nearly equivalent to 
Hirn's analysis, showed the heat yielded to or taken from the 
walls by the steam ; on the other hand the thermal measurements 
gave an indication of the heat gained by or yielded by the walls. 
The results are given in the following table; and considering the 
difficulty of the investigation and the large allowance for leakage, 
the concordance must be admitted to be very satisfactory. 

Table VII. 



INFLUENCE OF THE WALLS OF THE CYLINDER. 

Callendar and Nicolson, Proc. Inst. Civ. Engrs., 1897. 



Duration, minutes . . . 
Revolutions per minute . 
Mean gauge-pressure . . 
Gross steam per revolution 
Leakage correction . . . 
Net steam per revolution 
Steam caught at compression 
Weight of mixture in cylinder 
Indicated steam at quarter stroke 
Indicated steam at release . 
Increase of indicated weight 
Adiabatic condensation 
Indicated evaporation . 
Calculated evaporation 
Indicated condensation 
Calculated condensation 
Indicated horse-power 
Steam per H.P. per hour, pounds 



37 
43-8 
87.9 
o. 1422 
o. 1004 
0.0418 
0.0107 

0.0525 

0.0407 
o . 0466 
o . 0059 
0.0019 
0.0078 
0.0076 
0.0II8 
0.0148 
4.10 

26.8 



68 

45-7 

89.2 

0.1437 

0.0976 

0.0461 

0.0104 

0.0565 

0.0414 

0.0456 

0.0042 

0.0020 

0.0062 

0.0073 

0.0151 

0.0142 

4-34 

29. 1 



III. 



55 
47-7 
94.4 
0.1483 
0.0990 
o . 0493 
0.0103 
0.0596 
0.0437 
o . 0488 

0.0051 
0.0021 
0.0072 
0.0072 
0.0159 
0.0136 

4.78 

29-5 



IV. 



79 
70.4 
98.1 
o. 1094 
0.0697 
0.0397 
0.0099 
0.0496 
D.0418 
o . 0460 
0.0042 
0.0020 
0.0062 
o . 0048 
0.0078 
0.0092 
7.02 

23.8 



76 

73-4 
92.0 
1036 
0627 
0409 
0098 
0507 
0394 
0436 
0042 
0019 
0061 
0046 
0113 
0089 
6.67 
27.1 



VI. 



35 

81.7 

94.2 

o. 1000 

0.0576 

0.0424 

O.OIOO 

0.0524 
o . 0408 

0.0454 

o . 0046 
0.0020 
o . 0066 
0.0041 
0.0116 
o . 0080 

7.71 

26.9 



VII. 



25 

97 o 

96.0 
0.0856 
o . 0494 
0.0362 
0.0105 
0.0467 
0.0393 
0.0426 
0.0033 
0.0019 
0.0052 
0.0035 
0.0074 
0.0067 



CALLENDAR AND NICOLSON'S INVESTIGATIONS 



233 



The platinum thermometer near the cy Under- head showed 
superheating throughout compression, thus confirming our idea 
that steam can be treated as dry and saturated at the beginning 
of compression. This same thermometer fell rapidly during 
admission and showed saturation practically up to cut-off, as 
of course it should; after cut-off it began again to show a tem- 
perature higher than that due to the indicated pressure, which 
shows that the cylinder-head probably evaporated all the moisture 
from its surface soon after cut-off. If this conclusion is correct, 
there would appear to be little advantage from steam-jacketing 
a cylinder-head, a conclusion which is borne out by tests on the 
experimental engine at the Massachusetts Institute of Technology. 

The following table gives the areas, temperatures, and the heat 
absorbed during a given test by the various surfaces exposed to 
steam at the end of the stroke, i.e., the clearance surface. 

Table VIII. 

CYCLICAL HEAT-ABSORPTION FOR CLEARANCE SURFACES. 



Portions of surface considered. 


Area 
of surface, 
square feet. 


Mean 
temperature, 


Heat absorbed 

B.T.U. 

per minute. 


Cover face, 10.5 inches diameter . . 

Cover side, 3.0 inches 

Piston face, 10.5 inches diameter. . . 

Piston side, 0.5 inch 

Barrel side, 3.0 inches 

Counterbore, 0.5 inch 


0,60 
0. 70 
0.60 

O.ll 

0.71 
0.12 
0.90 


305 
305 
295 
295 
297 
291 

305 


68 

79 

no 

20 

"I 






Sums and means 


3-74 


301 


530 



The heat absorbed by the side of the cylinder wall uncovered 
by the piston up to 0.25 of the stroke was estimated to be 55 
B.T.U. per minute, which added to the above sum gives 585 b.t.u.; 
from which it appears that 90 per cent of the condensation is 
chargeable to the clearance surfaces, which were exceptionally 
large for this type of engine. Further inspection shows that 
the condensation on the piston and the barrel is much more 



234 INFLUENCE OF THE CYLINDER WALLS 

energetic than on the cover or head. For example, the face of 
the piston absorbs no b.t.u., while the face of the cover absorbs 
only 68 b.t.u., and the sides of the cover and of the barrel, each 
3 inches long, absorb 79 and 123 b.t.u. respectively. This 
relatively small action of the surface of the head indicates in 
another form that less gain is to be anticipated from the appli- 
cation of a steam-jacket to the head than to the barrel of a 
steam-engine. 

The exposed surfaces at the side of the cylinder-head and 
the corresponding side of the barrel are due to the use of a 
deeply cored head which protrudes three inches into the counter- 
bore of the cylinder, and which has the steam-tight joint at the 
flange of the head. It would appear from this that a notable 
reduction of condensation could be obtained by the 'simple expe- 
dient of making a thin cylinder-head. 

Leakage of Valves. — Preliminary tests when the engine was 
at rest showed that the valve and piston were tight. The valve 
was further tested by running it by an electric motor when the 
piston was blocked, the stroke of the valve being regulated so 
that it did not quite open the port, whereupon it appeared that 
there was a perceptible but not an important leak past the valve 
into the cylinder. There was also found to be a small leakage 
past the piston from the head to the crank end. 

But the most unexpected result was the large amount of leakage 
past the valve from the steam-chest into the exhaust. This was 
determined by blocking up the ports with lead and running the 
valve in the normal manner by an electric motor. This leak- 
age appeared to be proportional to the difference of pressure 
causing the leak, and to be independent of the number of 
reciprocations of the valve per minute. From the tests thus 
made on the leakage to the exhaust, the leakage correction in 
Table VII was estimated. Although the investigators concluded 
that their experimental rate of leakage was quite definite, it 
would appear that much of the discrepancy between the indicated 
and calculated condensation and vaporization can be attributed 
to this correction, which was two or three times as large as the 



LEAKAGE OF VALVES 235 

weight of steam passing through the cyhnder. Under the most 
favorable condition (for the seventh test) the leakage v^as 
0.0494 of a pound per stroke, and since there were 97 strokes 
per minute, it amounted to 

0.0494 X 97 X 60 = 287.5 

pounds per hour, or 32.6 pounds per horse-power per hour, so 
that the steam supplied per horse-power per hour amounted to 
56.4 pounds. If it be assumed that the horse-power is propor- 
tional to the number of revolutions, then the engine running 
double-acting will develop about 44 horse-power, and the leak- 
age then would be reduced to 6.5 pounds per horse-power 
per hour. Such a leakage would have the effect of increas- 
ing the steam-consumption from 23.5 to 30 pounds of steam per 
horse-power per hour. 

To substantiate the conclusions just given concerning the 
leakage to the exhaust, the investigators made similar tests on 
the leakage of the valves of a quadruple-expansion engine, which 
had plain unbalanced slide-valves. The valves chosen were the 
largest and smallest; both were in good condition, the largest 
being absolutely tight when at rest. Allowing for the size and 
form of the valve and for the pressure, substantially identical 
results were obtained. 

The following provisional equation is proposed for calculat- 
ing the leakage to the exhaust for slide-valves: 

leakage = -y-, 

where / is the lap and e is the perimeter of the valve, both in 
inches, and p is the pressure in pounds in the steam-chest in 
excess of the exhaust-pressure. The value of the constant 
in the above equation is 0.021 for the high-speed engine used by 
Callendar and Nicolson, and is 0.019 ^^^ ^^^ test each of the 
valves for the quadruple engine, while another test on the large 
valve gave 0.021. 



236 INFLUENCE OF THE CYLINDER WALLS 

This matter of the leakage to the exhaust is worthy of further 
investigation. Should it be found to apply in general to slide- 
valve and piston- valve engines it would go far towards explaining 
the superior economy of engines with separate admission- and 
exhaust-valves, and especially of engines with automatic drop- 
cut-off valves which are practically at rest when closed. It 
may be remarked that the excessive leakage for the engine 
tested appears to be due to the size and form of valves. The 
valve was large so as to give a good port-opening when the cut-off 
was shortened by the fly-wheel governor, and was faced off on 
both sides so that it could slide between the valve-seat and a 
massive cover-plate. The cover-plate was recessed opposite 
the steam-ports, and the valve was constructed so as to admit 
steam at both faces; from one the steam passed directly into the 
cylinder, and from the other it passed into the cover-plate and 
thence into the steam-port. This type of valve has long been 
used on the Porter- Allen and the Straight-line engines ; the former, 
however, has separate steam- and exhaust-valves. Such a valve 
has a very long perimeter which accounts for the very large effect 
of the leakage. 

Callendar and Nicolson consider that the leakage is probably 
in the form of water which is formed by condensation of steam 
on the surface of the valve-seat uncovered by the valve, and say 
further, that it is modified by the condition of lubrication of 
the valve-seat, as oil hinders the leakage. 



CHAPTER XII. 

ECONOMY OF STEAM-ENGINES. 

In this chapter an attempt is made to give an idea of the 
economy to be expected from various types of steam-engines 
and the effects of the various means that are employed when 
the best performance is desired. 

Table X gives the economy of various types of engines, and 
represents the present state of the art of steam-engine construc- 
tion. It must be considered that in general the various engines 
for which results are given in the table were carefully worked up 
to their best performance when these tests were made. In 
ordinary service these engines under favorable conditions may 
consume five or ten per cent more steam or heat ; under unfavor- 
able conditions the consumption may be half again or twice as 
much. 

All the examples in the table are taken from reliable tests; a 
few of these tests are stated at length in the chapter on the influ- 
ence of the cylinder walls; others are taken from various series 
of tests which will be quoted in connection with the discussion 
of the effects of such conditions as steam-jacketing and com- 
pounding; the remaining tests will be given here, together with 
some description of the engines on which the tests were made. 
These tables of details are to be consulted in case fuller informa- 
tion concerning particular tests is desired. 

The first engine named in the table is at the Chestnut Hill 
pumping-station for the city of Boston. Its performance is 
the best known to the writer for engines using saturated steam. 
Some engines using superheated steam have a notably less steam- 
consumption; but the heat-consumption, which is a better criterion 
of engine performance for such tests, is little if any better. The 
first compound engine for which results are given, used 9.6 

237 



238 



ECONOMY OF STEAM-ENGINES 



Table X. 

EXAMPLES OF STEAM-ENGINE ECONOMY. 



Type of Engine- 



Triple-expansion engines : 

Leavitt pumping-engine at Chestnut Hil 

Sulzer mill-engine at Augsburg 

Experimental engine at the Massachusetts 

Institute of Technology 

Marine engine Inna 

Marine engine Meteor 

Marine engine Brookline 

Compound engines: 
Horizontal mill-engine: 

superheated 

saturated 

Leavitt pumping-engine at Louisville . . 

Marine engine Rush 

Marine engine Fusi Yama 

Simple engines, condensing: 

Corhss engine at Creusot 

Corliss engine without jacket 

Harris- Corliss engine at Cincinnati . . . 

Marine engine Gallatin 

Simple engines, non-condensing: 

Corliss engine at Creusot 

Corliss engine without jacket 

Harris-Corliss engine at Cincinnati . . . 

Harris-Corliss engine at the Massachusetts 
Institute of Technology 

Direct-acting steam-pumps: 

Fire-pump at the Massachusetts Institute 

of Technology 

at reduced power 

Steam- and feed-j)ump on the Minneapolis 
at reduced power 



« a, 



50.6 
56 

92 
61 

72 
94 



128 
T27 
18.6 



60 

59 
76 

51 

63 
61 

76 



=QO 



« CO-" 

So 



176 

149 

147 

165 
145 
154 



135 

135 

137 

69 

57 



61 
96 
65 

104 

78 
96 

77 



47 
59 



576 
1823 

125 

645 

1994 

1136 



115 
127 

643 
266 

371 



176 
150 
145 
260 

237 
209 
120 

16 



41 
6.8 
8.8 
1.6 



£5 

O O 



SI 



11.2 

II-3 
13-7 

134 
15.0 

15-5 



9.6 
II. 8 
12.2 
18.4 
21 .2 



16.9 
18. 1 
19.4 
22 

21.5 
24. 2 
23-9 

33-5 



67 
125 

91 
243 



u s 

u o • 

Ho 1) 

.-= a. 



204 



231 



263 



199 
213 
222 



;48 



mo 

2070 






1.46 
2.01 
2 



pounds of steam and 199 b.t.u. per minute, the gain being 
hardly more than the variation that might be attributed to differ- 
ence in apparatus, etc. The Chestnut Hill engine, which was de- 



* Strokes per minute. 



TRIPLE-EXPANSION LEAVITT PUMPING-ENGINE 



239 



signed by Mr. E. D. Leavitt, has three vertical cylinders with their 
pistons connected to cranks at 120°. Each cylinder has four 
gridiron valves, each valve being actuated by its own cam on a 
common cam-shaft; the cut-off for the high-pressure cylinder is 
controlled by a governor. Steam-jackets are applied to the 
heads and barrels of each cylinder, and tubular reheaters are 
placed between the cylinders. Steam at boiler-pressure is sup- 
plied to all the jackets and to the tubular reheaters. 



Table XI. 

TRIPLE-EXPANSION LEAVITT PUMPING-ENGINE AT THE 
CHESTNUT HILL STATION, BOSTON, MASSACHUSETTS. 

CYLINDER DIAMETERS 1 3. 7, 24.375, AND 39 INCHES; STROKE 6 FEET. 

By Professor E. F. Mii,ler, Technology Quarterly, vol. ix; p. 72. 

Duration, hours 24 

Total expansion 21 

Revolutions per minute 50 -6 

Steam-pressure above atmosphere, pounds per square inch i75-7 

Barometer, pounds per square inch 14.9 

Vacuum in condenser, inches of mercury 27.25 

Pressure in high and intermediate jacket and reheaters, pounds per 

square inch 1 75 • 7 

Pressure in low-pressure jacket, pounds per square inch 99-6 

Horse-power , . . > 575-7 

Steam per horse-power per hour, pounds 11. 2 

Thermal units per honse-power per minute . . 204.3 

Thermal efficiency of engine, per cent , 20.8 

EflSciency for non-conducting engine, per cent . 28.0 

Ratio of eflSciencies, per cent 74 

Coal per horse-power per hour, pounds 1.146 

Duty per 1,000,000 b.t.u 141,855,000 

Efficiency of mechanism, per cent ..... 89 . 5 



The Sulzer engine at Augsburg has four cylinders in all, a high- 
pressure, an intermediate, and two low-pressure cylinders. The 
high-pressure cylinder and one low-pressure cylinder are in line, 
with their pistons on one continuous rod, and the intermediate 



240 



ECONOMY OF STEAM-ENGINES 



cylinder is arranged in a similar way with the other low-pressure 
cylinder. The engine has two cranks at right angles, between 
which is the fly-wheel, grooved for rope-driving. Each cylinder 
has four double-acting poppet-valves, actuated by eccentrics, 
links, and levers from a valve-shaft. The admission-valves 
are controlled by the governors. Four tests were made on this 
engine, as recorded in Table XII. 



Table XII. 

TRIPLE-EXPANSION HORIZONTAL MILL-ENGINE. 

CYLINDER DIAMETERS 29.9, 44.5, AND TWO OF 5 1. 6 INCHES; STROKE 78.7 

INCHES. 

Built by SuLZER of Winterthur, Zeitschrift des Vereins Deutscher Ingenieure, 

vol. xl, p. 534. 



Duration, minutes 

Revolutions per minute 

Steam-pressure, pounds per square inch . 

Vacuum, inches of mercury 

Horse-povi^er 

Steam per horse-power per hour, pounds 

Mean for four tests . . . . 1 1 . 46 . . 
Coal per horse-power per hour, pounds 

Mean for four tests .... i . 30 . . 
Steam per pound of coal 



I 


II 


III 


306 


322 


272 


56.23 


56.28 


56.18 


145-4 


147-9 


148.4 


27.24 


27.20 


27.20 


1872 


1835 


1850 


11-53 


11.49 


11.49 


1-37 


1.36 


1.29 


8.78 


8.49 


8.97 



IV 



327 

56.18 

149.0 
27.19 
1823 



1.19 
9. 62 



The test on the experimental engine at the Massachusetts 
Institute of Technology is quoted here because its efficiency 
and economy are chosen for discussion in Chapter VIII. Taking 
its performance as a basis, it appears on page 148 that with 150 
pounds boiler-pressure and 1.5 pounds absolute back-pressure 
such an engine may be expected to give a horse-power for 11. 5 
pounds of steam, from which it appears that under the same 
conditions its performance compares favorably with the Sulzer 
engine or even the Leavitt engine. 



MARINE-ENGINE TRIALS 



241 



Table XIII. 

MARINE-ENGINE TRIALS. 



By Professor Alexander B. W. Kennedy, Proc. Inst. Mech. Engrs., 1889-1892; 
summary by Professor H. T. Beare, 1894, p. t,t^. 



Triple or compound 

Diameter high-pressure cylinder, inches 

Diameter intermediate cylinder, inches = 

Diameter low-pressure cylinder, inches ...... 

Stroke, inches 

Duration of trial, hours 

Number of expansions 

Revolutions per minute , 

Steam-pressure above atmosphere, pounds per square 

inch 

Pressure in condenser, absolute, pounds per square 

inch 

Back-pressure, absolute, pounds per square inch . . . 

Horse-power 

Steam per horse-power per hour, pounds 

Thermal units per horse-power per minute 

Coal per horse-power per hour, pounds 

Steam evaporated per pound of coal 

Weight of machinery per horse-power, pounds . . . 



C. 

27.4 



50-3 

3,2> 

14 
.6.1 

55-6 

56.8 



2.32 
3-8 

371 
21. 2 

380 
2.66 
7.96 

603 



C. 

30 



57 
36 
10.9 
6.1 
86 

80. cr 



2.51 

3-4 
1022 

2T.7 
398 
2.9 

7-49 
448 



> 



C. 

50.1 



97.1 
72 
9 

5-7 
36 

105.8 

4.72 
6.0 
2977 
20.8 
367 
2.3 
8.97 
272 



T. 
29.4 
44 
70. 1 
48 

17 

10.6 

71.8 

145-2 

2-73 
3-3 
1994 
15.0 
265 
2.01 
7.46 
439 



T. 
21 .9 

34 

57 

39 

16 
19.0 
61. 1 

165 

o. 70 
1.8 

645 
13-4 

250 
1 .46 

9-15 
701 



The engines of the S. S. lona have an unusually large expansion 
and give a correspondingly good economy. The engines of the 
Meteor and of the Brookline give the usual economy to be 
expected from medium-sized marine engines. Table XIII 
gives details of tests on the engines of the first two ships 
mentioned, together with tests on compound marine engines. 
Table XIV gives tests on the engine of the Brookline. It 
appears probable that the relatively poor economy of marine 
engines compared with stationary engines is due to the 
smaller degree of expansion, which is accepted to avoid using 
large and heavy engines. 



242 



ECONOMY OF STEAM-ENGINES 



Table XIV. 

TESTS ON THE ENGINE OF THE S. S. BROOKLINE. 

CYLINDER DIAMETERS 23, 35, AND 57 INCHES; STROKE 36 INCHES. 

By F. T. Miller and R. G. B. Sheridan, Thesis, 1895, M.I.T. 



Duration, hours 

Revohitions per minute 

Steam-pressure, pounds per square inch above at- 
mosphere 

Vacuum, inches of mercury 

Horse-power 

Steam per horse-power per hour, pounds .... 

Coal per horse-power per hour, pounds 

B.T.U. per horse-power per minute 



94.6 

155 
21.6 
1242 
17.2 

2.22 
292 



2 
93-6 

155 
21.0 
1221 
16.9 

2. 17 
288 



III 


IV 


I 


3i 


93-^ 


93 


IS4 


145 


22.2 


21.7 


1136 


1137 


15-5 


17.0 


1.99 


2.18 


263 


288 



2h 

93 

148 

20.9 

1148 

16.3 

2.09 

277 



The horizontal mill-engine which heads the list of compound- 
engines in Table X, is a tandem engine for which particulars 
are given in Table XXVI on page 273. Its performance with 
superheated steam is the best among the engines named, and 
with saturated steam is a trifle superior to that of the Louisville 
engine. 

Table XV. 

COMPOUND LEAVITT PUMPING-ENGINE AT LOUISVILLE, 
KENTUCKY. 

CYLINDER DIAMETERS 27.2 AND 54.I INCHES; STROKE lO FEET. 

By F. W. Dean, Trans. Am. Soc. Mech. Engrs., vol. xvi, p. 169. 

Duration, hours - 144 

Revolutions per minute 18.6 

Pressures, pounds per square inch: 

Barometric 14.6 

Boiler above atmosphere 140 

At engine above atmosphere 137 

Back-pressure, l.p. cyHnder 0.95 

Total expansions 20 

Moisture in steam, per cent 0.55 

Horse-power 643.4 

Steam per horse-power per hour, pounds 12.2 

B.T.U. per horse-power per minute 222 

Thermodynamic efficiency, per cent 19 

Mechanical efficiency, per cent 93 

This engine has two cylinders, each jacketed with steam at 
boiler-pressure on barrels and heads, and steam at the same 
pressure is used in a tubular reheater. Each cylinder has four 
gridiron valves actuated by as many cams on a cam-shaft. 



AUTOMATIC CUT-OFF ENGINES 



243 



Table XVII. 

ENGINES OF THE U. S. REVENUE STEAMERS RUSH AND 

GALLATIN. 



Diameters of cylinders, inches 

Stroke, inches 

Duration, hours 

Revolutions per minute 

Steam-pressure by gauge, pounds . . . . 

Vacuum, inches of mercury 

Total expansions 

Horse-power 

Steam per horse-power per hour, pounds 



Rash. 




Gallatin. 


24 and 


38 


34.1 


27 




30 


55 




24 


71 




51 


69.1 




65.4 


26.5 




25.1 


6.2 




4.5 


266.5 




260.5 


18.4 




22 



The details of the tests on the U. S. Revenue Steamers Rush 
and Gallatin are given in Table XVII, as made about 1875 ^Y 
a board of naval engineers to determine the advantages of com- 
pounding and using steam-jackets. Three other engines were 
tested at the same time, but they were of older types and are less 
interesting. 

A remarkably complete and important series of tests was made 
in 1884 by M. F. Delafond. These tests are recorded in Tables 
XXX and XXXI, from which there are quoted in Table X four 
results with and without condensation and with and without 
steam in the jackets. 

Table XVIII. 

AUTOMATIC CUT-OFF ENGINES. 

CYLINDER DIAMETERS 1 8 INCHES; STROKE 4 FEET. 

By J. W. Hill. 
(First Millers' International Exhibition, Cincinnati, 1880.) 



Duration 

Cut-off 

Revolutions per minute 

Boiler-pressure alx>vc atmos.Jbs. per sq. in 

Barometer, inches of mercury 

Vacuum, inches of mercury 

Back-pressure, absolute, lbs. per sq. in. . 

Horse-power 

Steam per horse-power per hour, pounds 
B.T.U. per horse-power per hour . . . 





Condensing. 


Non-condensing. 


R. 


H. 


W. 

10 


R. 


H. 


W. 


10 


10 


9 


10 


10 


0.124 


0.119 


0.131 


0. 160 


0.136 


0.170 


75.4 


75-8 


74.5 


75-3 


75-8 


76.1 


95-8 


96.1 


96.3 


96.6 


96.3 


96.3 


29.7 


29.6 


29.4 


29.8 


29.6 


29-5 


25-5 


257 


24.0 








4.5 


3-4 


4-7 


15-S 


14-9 


15-5 


143-2 


145. 1 


143-9 


121. 7 


119-7 


126.7 


20.6 


19.4 


19-S 


25-9 


23-9 


24.9 


372 


349 


343 


433 


400 


415 



244 



ECONOMY OF STEAM-ENGINES 



The details of the tests on the Harris- Corliss engine at Cin- 
cinnati, together with tests on two similar engines, are given in 
Table XVIII. 

Table XIX. 

DUPLEX DIRECT-ACTING FIRE-PUMP AT THE MASSACHUSETTS 
INSTITUTE OF TECHNOLOGY. 

TWO STEAM-CYLINDERS 1 6 INCHES DIAMETER, 12 INCHES STROKE. 

Technology Quarterly, vol. viii, p. 19. 



Single 
strokes 


Length 
of stroke. 


Length 
of stroke. 


Steam- 
pressure 


Horse- 
power. 


Horse- 
power. 
Water- 


Steam 
per horse- 


B.T.U. 
per horse- 


Duty. (Foot- 
pounds per 


per 


West. 


£ast 


by gauge. 


Steam- 


power per 


power per 


1 ,000, coo 


minute. 




cylinders. 


cylinders. 


hour. 


minute. 


B.T.U.) 


99 


11.40 


10. 10 


58.5 


6.78 




i25 


2070 


13,920,000 


TT4 


II. 70 


11.07 


55-6 


12.48 




lOI 


1674 


17,540,000 


119 


11.49 


11.07 


51-4 


12.18 




109 


1809 


16,980,000 


135 


11.60 


II. 10 


53-8 


18.24 




92 


1530 


19,850,000 


156 


10.90 


10. 26 


47-2 


21.00 


IQ.80 


98 


1619 


18,280,000 


193 


10.09 


10.31 


45.6 


32-9.5 




78 


1291 


23.73o>ooo 


'P 


11-77 


11.79 


45.6 


39-55 




66 


1083 


27,980,000 


180 


11.74 


11.66 


46.5 


41.20 




67 


IIIO 


27,030,000 



Table XX. 

TESTS OF AUXILIARY STEAM MACHINERY OF THE U. S. 

MINNEAPOLIS. 
By P. A. Engineer W. W. White, U. S. N., Journal Am. Sac. Naval 
Engrs., vol. x. 



S. 



Engine or pump tested. 



Centre circulating-pump: 

Full power 

Reduced power* . . . 
Starboard circulating-pump: 
Reduced power .... 
Starboard air-pump . . . 
Centre air-pump f . . • . 
Water-service pump . . . 
Fire- and feed-pump . . . 

Do 

Do 

Do 

Fire-and bilge-pump . . . 

Blower-engine 

Dynamo-engine 

Do 

Ice-machine engine .... 



O 13 
. C 



14 

5 
10.5 
10.5 

7 



as '^ 

0-0 

- C 



o.S 



5 a 



7-S 
10.9 

t2.0 

10 

10.8 

11.2 

4 
5 
5 



^ in 

O C 

<0 "*J 4J 



^ E 



171. 6 
90 

82 
16.6 

IS-2 
40.9 
12.7 

37-3 

II. o 

2.6 

27.7 
595 
425 
425 
73-1 


























.s 


g 


'^ C 






'S 


ii% 


2 

3 


^a 


« 


c 


3-7 


18.9 


2-50 


4.1 


3-28 


2.0 


2-58 


6.5 


3-2 


25-2 


2-59 


1.04 


3-31 


0.78 


1-46 


6.4 


2-23 


8.8 


3-27 


1.6 


2-2 


2.5 


1-24 


16.3 


l-IO 


22.9 


0-26 


35-2 


5-12 


6.0 






125 

183 

78 

205 

319 

156 

91 

243 

171 

77 

65 

56 



* One cylinder only supplied with steam. 

t Pump loaded with three times the power developed during official trial, when main engine 
indicated 7219 H.P. 



METHODS OF IMPROVING ECONOMY 



245 



The two tests on the direct-acting fire-pump at the 
Massachusetts Institute of Technology are taken from Table 
XIX, and the tests on the feed- and fire-pump on the Minneapolis 
are given in Table XX. Both sets of tests show the extravagant 
consumption of steam by such pumps when running at reduced 
powers. The latter table is most interesting on account of the 
light that it throws on the way that coal is consumed by a war- 
vessel when cruising at slow speeds or lying in harbor. 

Methods of Improving Economy. — The least expensive type 
of engine to build is the simple non-condensing engine with slide- 
valve gear; this type is now used only where economy is of little 
importance, or where simplicity is thought to be imperative. 
Starting with this as the most wasteful type of engine, improve- 
ments in economy may be sought by one or more of the following 
devices : 

1. Increasing steam-pressure. 

2. Condensing. 

3. Increasing size. 

4. Expansion. 

5. Compounding. 

6. Steam-jackets. 

7. Superheating. 

8. The binary engine. 

An investigation of the conditions under which these various 
devices can be used to advantage, of the gain to be expected, 
and of their limitations, is one of the most interesting and impor- 
tant problems for the engineer. For the student the process of 
such an investigation is even of more importance than the 
conclusions, because by it he may learn to form his own opinions 
and may take account of other tests as they may be presented. 
The order chosen is to some extent arbitrary, and cannot be 
adhered to strictly, as the tests on which the investigation is 
based were made for various purposes, and combine the several 
devices in various manners. 

Of these devices the first two and the last are clearly methods 
of extending the temperature-range, and are indicated directly 



246 ECONOMY OF STEAM-ENGINES 

by the ideas that have been presented in the general discussion 
of thermodynamics, and in particular by the adiabatic theory of 
the steam-engine; the fourth (expansion) may almost be included 
in this category as a means of making the extension of temperature- 
range effective. It has been seen that the necessity of making 
the cylinder of metal which is a good conductor and has an 
energetic action on the steam in the cylinder, interferes v^rith our 
attempts to approach the efficiency that can . be computed for 
non-condensing engines, and places limitations on the advantages 
to be gained by increasing the temperature-range. The other 
devices enumerated (increase of size, compounding, steam- 
jackets, and superheating) are various methods v^hich have 
been applied to diminish the influence of the cylinder v^^alls, 
and allovv^ us to take advantage of a large temperature-range. It 
appears at first sight that superheating should be included in 
the first category, as it clearly does increase the temperature- 
range betw^een the steam-pipe and the exhaust-pipe of the engine, 
but the steam in the cylinder is seldom superheated at cut-off, 
and it is better to consider this device as a means of reducing 
cylinder condensation. 

It is interesting to consider that condensation, expansion, and 
steam-jackets v^ere used by Watt for his earliest engines, and that 
he wsis limited in pressure by the condition of the art of engineer- 
ing, so that there was no occasion for compounding; his cylinders 
also had considerable size, though the powers of the engines 
would not now appear to be large. In the course of his develop- 
ment of the true steam-engine from the atmospheric engine, 
which had the steam condensed in the cylinder by spraying in 
water, Watt's attention was especially directed to the influence 
of the cylinder walls ; he also made experiments on the properties 
of saturated steam within the range of available pressures, and 
had such an appreciation of the conditions of his problem that 
little was left to his successors except to learn how to use the 
higher steam-pressures which the developments of metallurgy 
and machine-shop practice made possible. The fact that our 
theory of the steam-engine was developed after his time, and 



EFFECT OF RAISING STEAM-PRESSURE 247 

that the theory has sometimes been misappHed, has given an 
erroneous opinion that the steam-engine has been developed 
without or in spite of thermodynamics. And further, his use of 
all the advantages then available has had a tendency to obscure 
their importance, and makes it the more desirable to state the 
several methods categorically as given above. 

It is now commonly considered that the steam-engine has 
been brought to full development, and that there is little if any 
substantial improvement to be expected; in fact, this condition 
was reached a decade or two ago, when the triple engine using 
steam at 150 to 175 pounds by the gauge, was perfected. The 
most recent change is the use of superheated steam at high 
pressures, now that effective and durable superheaters have 
been devised. Experiment and experience have settled fairly 
well the limitations for the various methods of improving economy 
and allow of a fair and conservative presentation to which there 
will probably be few exceptions. We will, therefore, state the 
general conclusions as briefly as may be, and give the tests on 
which they may be based. 

In order to bring out the advantage to be obtained by a certain 
device, such as compounding, we will compare only the best 
performance of the simple engine with the best performance of 
the compound engine, each being given all the advantages that 
it can use. The fact that marine compound engines have a 
worse economy than stationary simple-engines, has no other 
meaning for our present purpose, than that engines on ship- 
board are subject to unfavorable limitations. 

Effect of Raising Steam-Pressure. — A glance at the table on 
page 148 which gives the efficiency for Carnot's cycle, will show 
that if we begin with a low steam-pressure, there is a large advan- 
tage from increasing the pressure and consequently the tem- 
perature-range, but that this advantage becomes progressively 
less marked. This conclusion is of course immediately evident 
from the efficiency for Carnot's cycle, which may be written 

T - T 

e = -,= 



248 ECONOMY OF STEAM ENGINES 

If /' is taken to be 100° F., and if / is made successively 200°, 
300°, and 400°, the values of the efficiency are 0.15, 0.26, and 0.35. 
But the influence of the cyUnder quickly puts a stop to this 
improvement unless we resort to compounding, as will be seen by 
"studying Delafond's tests in Table XXI, page 250, and by 
Figs. 57 and 58 on pages 252 and 253, in which the steam-con- 
sumption is plotted as ordinates on the fraction of the stroke at 
cut-off, each curve being lettered with the steam-pressure which 
was maintained while a series of tests was made. Fig. 57 rep- 
resents tests without steam in the jackets, and Fig. 58, tests with 
steam in the jackets. Those curves bearing the letter C were 
with condensation, and those bearing the letter N were non- 
condensing. Inspection of Fig. 57 shows a progressive reduc- 
tion in steam-consumption, as the pressure is increased from 
35 pounds by the gauge to 60 pounds for the condensing engine 
without a steam-jacket, but raising the pressure from 60 pounds 
to 80 and 100 pounds gives a marked increase in steam-con- 
sumption. The same figure indicates that 100 pounds is probably 
the limit for non-condensing, unjacketed engines. The curves 
on Fig. 58 are not quite so conclusive; but we may from both 
figures give the following as the best pressures to be used with 
simple engines of good design and automatic valve-gear: 

Desirable Pressures for Simple Engines. 

Condensing, without steam-jackets, 60 pounds gauge. 

Condensing, with steam-jackets, 80 pounds gauge. 

Non-condensing, without steam-jackets, 100 pounds gauge. 

Non-condensing, with steam-jackets, 125 pounds gauge. 

Delafond's Tests. — In 1883 an extensive and important 
investigation was made by Mons. F. Delafond on a horizontal 
Corliss engine at Creusot to determine the conditions under 
which the best economy can be obtained for such an engine. 
The engine had a steam-jacket on the barrel, but was not jacketed 
on the ends. Steam was supplied to the jacket by a branch 
from the main steam-pipe, and the condensed water was drained 
through a steam-trap into a can, so that the amount of steam 



DELAFOND'S TESTS 249 

used in the jacket could be determined. The engine was tested 
with and without steam in the jacket, both condensing and non- 
condensing, and at various pressures from 35 to 100 pounds 
above the pressure of the atmosphere. The effective power 
and the friction of the engine were also obtained by aid of a 
friction-brake on the engine-shaft. 

The piping for the engine was so arranged that steam could be 
drawn either from a general main steam-pipe or from a special 
boiler used only during the test. Before making a test the 
engine, which had been running for a sufficient time to come 
to a condition of thermal equilibrium, was supplied with steam 
from the general supply. At the instant for beginning the test 
the general supply was shut off and steam was taken from the 
special boiler during and until the end of the test, and then the 
pipe from that boiler was closed. The advantage of this method 
was that at the beginning and end of the test the water in the 
boiler was quiescent and its level could be accurately determined. 
At the end of a test the water-level was brought to the height 
noted at the beginning. The water required for feeding the 
special boiler during the test and for adjusting the water-level 
at the end was measured in a calibrated tank. As the steam- 
pressure in the general-supply main and in the special boiler 
was the same, there was little danger of leakage through the 
valves for controlling the steam-supply; the regularity and con- 
sistency of results shown by the curves of Figs. 57 and 58 attest 
to the skill and accuracy with which these tests were made. 

Table XXI gives the results of tests made with condensation, 
and Table XXII gives the results of tests without condensation. 
All the tests both with and without condensation, but during 
which no steam was used in the jackets, are represented by the 
several curves of Fig. 57, while Fig. 58 represents tests made 
with steam in the jackets. The curves are lettered to show the 
mean steam-pressure for the series represented and the condition, 
whether with or without condensation. Thus on Fig. 57 the 
lowest curve 60C represents tests made without steam in the 
jackets and with condensation, while the highest curve on Fig. 



250 



ECONOMY OF STEAM-ENGINES 



58 represents tests with steam in the jackets and without con- 
densation, at 50 pounds boiler-pressure. The abscissae for the 
curves are the per cents of cut-off, and the ordinates are the 
steam-consumptions in pounds per horse-power per hour. The 

Table XXI. 

HORIZONTAL CORLISS ENGINE AT CREUSOT. 

CYLINDER DIAMETER 21. 65 INCHES; STROKE 43-31 INCHES; JACKET ON 
BARREL only; CONDENSING. 

By F. Delafond, Annates du Mines, 1884. 



Number 
of test. 


Duration, 
minutes. 


Revolu- 
tions per 
minute. 


Cut-off in 

per cent of 

stroke. 


Steam- 
pressure, 
pounds per 
sq. in. 


Vacuum, 
inches of 
mercury. 


Steam 

used in 

jacket, 

per cent. 


Indicated 
horse- 
power. 


Steam per 
horse, 
power 

per hour, 
pounds. 


I 


60 


60.0 


4 


96.3 


27.1 




109 


23.2 


2 


105 


58.6 


6 


98.8 


27.1 




128.5 


22.2 


3 


75 


59-4 


9 


100 


27.0 




161 


21.4 


4 


36 


57-7 


12.5 


99.1 


27.0 




i86 


22.0 


5 


73 


58.8 


5-5 


104 


27.4 


'?' 


141 


17.1 


6 


55 


61.5 


6.7 


102.4 


27.1 


? 


159- 5 


16.7 


7 


80 


59-9 


6.7 


103.8 


27.4 


2.9 


155 


16.5 


8 


39 


S8.i 


12.5 


105.2 


26.8 


3.2 


212 


17.6 


9 


120 


59.8 


7.5 


79.8 


27.1 




126 


21.2 


10 


100 


59-3 


8.3 


81.1 


27.4 








134 


21. 1 


n 


90 


59.8 


10.5 


80.1 


27.1 








150 


20.8 


12 


55-5 


58.0 


14 


85.5 


27.1 








17s 


19.9 


13 


50 


59- 1 


18 


84.8 


26.5 








194 


20.4 


14 


94 


59-6 


5 


8s. I 


27.4 


3.0 


1X2 


17.7 


15 


102 


59-6 


5-5 


83.3 


27.6 


3.1 


124 


17.3 


16 


40 


59.4 


II-5 


84.1 


27.1 


1.2 


176 


16.9 


17 


40 


60 


14 


84.1 


27.0 


IS . 


193 


17-S 


18 


91 


58.3 


5-9 


60.5 


28.0 




85.3 


20.4 


19 


90 


59-5 


9 


55.8 


27.6 








IIS 


19.1 


20 


75 


59.0 


15-5 


61.2 


27.8 








ISO 


18. 1 


21 


75 


58.3 


22.7 


58.3 


27.6 








172 


18.4 


22 


31 


59.2 


25 


61.2 


27.1 








i86 


18.8 


23 


IIS 


59-9 


6 


59-9 


27.8 


2.5 


91.7 


18.5 ■ 


24 


92 


59-6 


9 


59-9 


27.4 


2.5 


117 


17.6 


25 


90 


58.8 


15-5 


60.9 


27.1. 


1.8 


ISO 


173 


26 


71 


59- 1 


20 


61.9 


26.8 


i-S 


175 


17.7 


27 


50 


590 


25 


62.3 


26.4 


1.6 


194 


18.6 


28 


70 


60.7 


6 


45 -o 


28.0 




75.6 


20.7 


?9 


80 


58.8 


9-5 


48.9 


28.1 








94.3 


19.4 


30 


III 


60.4 


15 


47-9 


27.6 








120 


18.8 


31 


54 


58.8 


21 


47.8 


27.6 








140 


19.0 


32 


55 


59.4 


29 


47.6 


27.1 








i6s 


19.8 


33 


98 


60.3 


5 


45.8 


28.0 


2.6 


68.8 


19.3 


34 


63 


57. '^ 


10 


51.6 


27.6 


2-3 


95-5 


18. 5 


35 


60 


59.7 


14-3 


49.1 


28.1 


1.4 


120 


18.2 


36 


74 


60.1 


22 


48.6 


27.8 


1.4 


152 


18.9 


37 


50 


59- 5 


29 


50.2 


26.8 


1.2 


179 


19.7 


38 


85 


60.3 


18.2 


33- 1 


27.8 




io6 


20.5 


39 


68 


61. 1 


43 


34-7 


26.5 




160 


22.7 


40 


42.5 


61.0 


56.7 


36.3 


26.0 




181 


25-3 


41 


20 


60.0 


100 


31.7 


25.2 




182 


35. 9 


42 


73 


60.7 


19 


32.0 


27.6 


V.6 


III 


19.8 


43 


80 


61.9 


42 


33-0 


26.5 


I.I 


162 


22.1 


44 


40 


61. 1 


58 


35.1 


26.0 


0.6 


180 


25.4 


45 


25 


60.4 


100 


34.7 


25.2 


c 


).; 


' 


199 


33.0 



DELAFOND'S TESTS 



251 



results for individual tests are represented by dots, through 
which or near which the curves are drawn. As there are only 
a few tests in any series, a fair curve representing the series can 
be drawn through all the points in most cases. The exceptions 

Table XXII. 

HORIZONTAL CORLISS ENGINE AT CREUSOT. 

cylinder diameter 2 1. 65 inches; stroke 43. 3 1 inches; jacket on barrel 

only: non-condensing. 





B 


y F, Delapond, Annates des Mities, 1884. 




Number of 
test. 


Duration, 
minutes. 


Revolu- 
tions per 
minute. 


Cut-off in 

per cent of 

stroke. 


Steam- 
pressure, 
pounds per 
square inch. 


Steam used 
in jacket, 
per cent. 


Indicated 
horse- 
power. 


Steam per 

horse-power 

per hour, 

pounds. 


I 


78 


61.7 


13 


96.3 




147-5 


28.4 


2 


55 


61.4 


17 


100.2 




181. s 


26.8 


3 


25 


63.6 


20 


102.0 




217 


25.8 


4 


80 


60.8 


II 


98.1, 


2.5 


143 


22.8 


5 


60 


62.0 


13 


103.8 


3-4 


177.5 


22.1 


6 


36 


62.0 


16 


103.0 


3.1 


194 


22.4 


7 


30 


62.7 


20 


103-5 


2.0 


237 


21.5 


8 


66 


62.0 


15-5 


73-7 




121 


27.6 


9 


60 


60.9 


18 


77.0 




136 


26.7 


10 


60 


60.0 


24-5 


76.7 




178 


24.6 


II 


30 


60.6 


32 


77-5 




209 


24.2 


12 


70 


61. 1 


16.5 


77.0 


1-7 


137 


23-7 


13 


50 


61.6 


23-5 


75-8 


1.2 


180 


21.8 


14 


30 


60.5 


30 


78.0 


1-3 


204 


22.0 


15 


71 


61.4 


24.5 


50.8 




108 


27-3 


16 


70 


61. 1 


37 


51-2 




147 


27.2 


17 


50 


60.9 


58 


50-5 




173 


30.2 


18 


25 


60.6 


100 


34-9 




145 


46.8 


19 


70 


60.5 


23 


52.6 


1-5 


108 


25-3 


20 


60 


60.5 


34 


51.8 


I.I 


141-5 


25.2 


21 


50 


60.3 


58 


46.2 


0.7 


168.5 


28.7 


22 


30 


61. I 


100 


33-7 


0-3 


147-5 


46.3 



are tests made with condensation for boiler-pressure of 80 and 
100 pounds per square inch. The forms of the curves SoC 
and looC, Fig. 57, were made to correspond in a general way 
to the curves 50C and 60C. The discrepancies appear large 
on account of the large scale for ordinates, but they are not 
really of much importance; the largest deviation of a point from 
the curve looC is half a pound out of about 22, which amounts 
to little more than two per cent. On Fig. 58 the curve 80C is 
drawn through the points, but though its form does not differ 



252 



ECONOMY OF STEAM-ENGINES 



radically from the curves 6oC and 50C, so marked a minimum 
at so early a cut-off is at least doubtful. Considering that the 
probable error of determining power from the indicator is about 



30 
28 
26 
24 
22 
20 
18 












y 




\ 






-py 


/ 




\ 






y 






N 


\ 


~j. 




/ 


\ 








^ 




< 












\ 




::^ 










bOC 











10 



20 



30 



Fig. 57. 



40 



50 



two per cent, it would not be difficult to draw an acceptable 
curve in place of 80C which should correspond to the forms of 
60C and 50C. 

The results of the four tests made with steam in the jacket 
and with condensation, and which are numbered 5, 6, 7, and 8, 
in Table XXII, are represented by dots inside of small circles 



CONDENSATION 253 

on Fig. 58. It does not appear worth while to try to draw a 
curve to represent these tests. 

Condensation. — The complement of raising the steam-pressure 



30 



26 



24 



22 



20 



18 



16 

























/ 










^ 


/ 












/ 




v^ 


% 




y" 






'V 


^ 


^ 






\ 


^ 

^G 


V 










^^ 


/^ 









10 



30 
Fig. 58. 



40 



50 



tiO 



is the use of a condenser with a good vacuum. The advantage 
to be obtained by this means can be determined from Delafond's 
tests by aid of Figs. 57 and 58; taking the best conditions as 
already recorded in Table X, the engine without a jacket and 
without a vacuum used 24.2 pounds of steam per horse-power 
per hour, and with a vacuum it used 18. i pounds; with steam in 
the jackets the results were 21.5 and 16.9. A direct comparison 



254 ECONOMY OF STEAM-ENGINES 

of either pair of results would appear to give a saving of about 
25 per cent, which would be manifestly misleading. The results 
of brake tests for this engine on page 273, show that the mechan- 
ical efficiency when running non-condensing was 0.90, but that 
it was only 0.82 when running condensing. The steam per 
brake horse-power per hour can be obtained by dividing the 
indicated steam by the mechanical efficiency, so that the above 
pairs of results became for the engine without steam in the jacket, 
non-condensing 26.9, and condensing 22.1, and for the engine 
with steam in the jacket, 23.9 and 20.6; so that the real gain 
from condensation was 

26.0 — 22.1 „ 2^.0 — 20.6 

— ^— = 0.18 or -^^-^ = 0.14. 

26.9 23.9 

The gain from condensation will vary with the type of engine 
and the conditions of service, and may be estimated from ten 
to twenty per cent. Clearly the gain is greater with a good 
vacuum than with a poor vacuum. There is, however, another 
feature which should be considered, namely, the mean effective 
pressure; when the conditions of service are such that the mean 
effective pressure is large, the gain from condensation and the 
advantage of maintaining a good vacuum are not so great as 
when the mean effective pressure is small. This feature can 
be best illustrated with examples of triple-expansion engines, 
which are able to work advantageously with a large total expan- 
sion, and for them we may deal with the reduced mean effective 
pressure, meaning by that expression the result obtained by the 
following process: the mean effective pressure for the high- 
pressure cylinder is to be multiplied by the area of that piston 
and divided by the area of the low-pressure piston; the mean 
effective pressure for the intermediate cylinder is to be treated 
in a similar way; the two results are then to be added to the 
mean effective pressure for the low-pressure cylinder; clearly 
this sum, which is called the reduced mean effective pressure, 
if it were applied to the low-pressure piston would develop the 
actual power of the engine. Now the reduced mean effective 



INCREASE OF SIZE 



255 



pressure for a pumping-engine or mill-engine may be as low as 
18 pounds per square inch, and a difference of one inch of 
vacuum (or half a pound of back-pressure)- will be equivalent 
to nearly three per cent in the power; on the other hand, a naval 
engine is likely to have a reduced mean effective pressure of 
forty pounds per square inch, and compared with it a difference 
of one inch of vacuum is equivalent to a little more than one per 
cent. In any case the gain in economy due to a small improve- 
ment in vacuum is approximately equal to the reduction in the 
absolute pressure in the condenser, divided by the reduced 
mean effective pressure. 

A very important matter is brought out in this discussion of 
the gain from condensation, namely, that the real gain is deter- 
mined by comparing the engine consumption for the net or 
brake horse-powers. The only reason for using the indicated 
power (as is most commonly done) is that the brake-power is 
often difficult to determine and sometimes impossible. As 
was pointed out on page 144, a true basis of comparison is the 
heat-consumption of the engines compared in b.t.u. per horse- 
power per hour. But that quantity was not determined for the 
tests by Delafond, and since the comparisons are for two pairs 
of tests, one pair with and the other without jackets there is no 
objection to it in the cases discussed. 

Increase of Size. — Since the failure to attain the economy 
computed for the non-conducting engine is due mainly to the 
action of the cylinder walls, and since the volume of the cylinder 
are proportional to the cube of a linear dimension, while the sur- 
face is only proportional to the square, a great advantage might 
be expected by simply increasing the size of the engine. Such 
an advantage is indicated by the comparison of the small Harris - 
Corliss engine at the Massachusetts Institute of Technology with 
the Corliss engine at Creusot, the steam-consumption without 
condensation or steam-jackets being 33.5 pounds and 24.2 pounds 
per horse-power per hour, and the gain from increase of 
size being 

-i-Z.K — 24.2 

33-5 



256 ECONOMY OF STEAM-ENGINES 

In this case the larger engine has about twelve times the cylinder 
capacity of the smaller one. This feature appears to depend on 
the absolute size of the engine, because, as will appear later, there 
is little if any advantage in speed of rotation within the usual 
limits of practice. 

But the advantage from increase of size soon reaches a limit, 
as will be apparent from the consideration that the best results 
in Table X are for engines of moderate power, judged by modern 
standards. These engines have the advantages of compounding, 
and of the use of steam-jackets or superheated steam; the advan- 
tages from jacketing or superheating decrease with the size, 
and such devices are possibly of little advantage to massive 
engines. 

Expansion. — There are two limits to the amount of expansion 
that can be advantageously used for a given engine: one limit 
is imposed by the action of the cylinder walls, and the other is 
imposed by the friction of the engine. Simple engines have the 
most advantageous point of cut-off determined by the first limit, 
which can be clearly determined by aid of Delafond's experi- 
ments; compound and triple- expansion engines so divide up 
the temperature-range that any desirable expansion can be 
employed. The terminal pressure at the end of expansion for 
a stationary, triple, or compound engine may be made as low as 
five pounds absolute; and as the back- pressure is likely to be 
a pound or a pound and a half, so that the terminal effective 
pressure is three and a half or four pounds, and as it takes about 
two pounds per square inch to drive the piston and connected 
parts, there is evidently little to be gained in economy by further 
expansion. 

As for simple engines, an inspection of Figs. 57 and 58 on pages 
252 and 253 shows that the best point of cut-off for non-conden- 
sing engines is one-third stroke, and for condensing engines about 
one sixth-stroke; if the engine has a steam-jacket, the cut-off 
may be a little earlier than one-sixth stroke, but there probably 
is little advantage from such an increase of expansion if we deal 
with the net or brake horse-power. 



COMPOUNDING 



257 



The total expansion for a compound or triple engine can be 
obtained in two ways: we may use a large ratio of the large 
cylinder to the small cylinder, or we may use a short cut-off for 
the high-pressure cylinder. The two methods may be illustrated 
by the two Leavitt engines mentioned in Table X; the ratio of 
.the large to the small cylinder of the compound engine at 
Louisville, is a trifle less than four, and the cut-off for the high- 
pressure cylinder is a little less than one- fifth stroke; on the 
other hand, the triple engine at Chestnut Hill has a little more 
than eight for the extreme ratio of the cylinders, and has the 
cut-off for the high-pressure cylinder at a little more than four- 
fifths. So large an extreme ratio as eight would not be con- 
venient for a compound engine, but ratios of five or six have 
been used, though not with the best results. 

Marine engines usually have comparatively little total expan- 
sion both for compound and for triple engines, and consequently 
are unable to work with an economy equal to that for stationary 
engines ; the type of valve-gear which the designers feel constrained 
to use is also little adapted to give the best results. There is 
some question whether there is not room for improvement in 
both these directions. 

Compounding. — The most efficacious method which has 
been devised to increase the amount of expansion of steam in 
an engine, and at the same time to avoid excessive cylinder- 
condensation, is compounding; that is, passing the steam in 
succession through two or more cylinders of increasing size. 
An engine with two cyHnders, a small or high-pressure cylinder 
and a large or low-pressure cylinder, is called a compound 
engine. An engine with three cylinders, a high-pressure cylinder, 
an intermediate cylinder, and a low-pressure cylinder, is called 
a triple-expansion engine. A quadruple engine has a high- 
pressure cylinder, a first and a second intermediate cylinder, 
and a low-pressure cylinder. Any cylinder of a compound or 
multiple-expansion engine may be duplicated, that is, may be 
replaced by two cylinders which are usually of the same size. 
Thus, at one time a compound engine with one high- pressure 



258 ECONOMY OF STEAM-ENGINES 

and two low-pressure cylinders was much used for large steam- 
ships. Many triple engines have two low-pressure cylinders, 
which with the high-pressure and the intermediate cylinders 
make four in all. Again, some triple engines have two high- 
pressure cylinders and two low-pressure cylinders and one 
intermediate cylinder, making five in all. 

Two questions arise: (i) Under what conditions should the 
several types of engines be used? and (2) What gain can be ex- 
pected by using compound or triple expansion ? 

Neither question can be answered explicitly. 

From tests already discussed and for which the main results 
are given in Table X, it appears that with saturated steam, the 
best results were attained with the following pressures : for triple 
engines about 175 pounds by the gauge, for compound engines 
145 pounds, and for simple engines with about 80 pounds; all 
for engines with condensation. Nearly as good results were 
obtained for a compound engine with 135 pounds pressure, 
and on the other hand the simple engine could use 100 pounds 
with equal advantage. The information concerning the simple 
engine is sufficient to serve as a reliable guide, but there is at 
least room for discretion concerning the best pressures for com- 
pound and triple engines. There will probably be little chance 
of serious disappointment if the following table is used as a guide 
in designing engines, all being with condensation and with 
steam-jackets. 

Best Gauge-Pressures for Steam- Engines. 

Simple 80 

Compound 140 

Triple 175 

If for any reason it is desired to use a higher or lower pressure 
in any case, a variation of 20 pounds either way may be assumed 
without much loss of efficiency; this, however, cannot be stated 
quantitatively at the present time. 

For non-condensing simple engines the pressure should 
preferably be 100 pounds without a steam-jacket, and 125 



COMPOUNDING 



259 



pounds with a steam-jacket ; with an allowable variation of twenty 
pounds. For a non-condensing compound engine we may take 
as the preferred pressure about 175 pounds, but our tests do not 
include this case, and the figure is open to question. There is 
little, if any, occasion for using triple-expansion non-condensing 
engines. 

About ten years ago an attempt was made to introduce quad- 
ruple-expansion engines, using steam at about 250 pounds for 
marine purposes in conjunction with water-tube boilers, which 
can readily be built for high-pressures ; but more recent practice 
has been to adhere to triple engines even where the designer 
has chosen a high-pressure for sake of developing a large power 
per ton of machinery, or for any other purpose. 

For convenience in trying to determine the gain from com- 
pounding, the following supplementary table has been drawn off. 



Data and Results. 



Revolutions per minute 

r-. above atmosphere, pounds 



Steam-pressure 

Total expansion 

Ste^m per horse-power per hour, pounds 

B.T.U. per horse-power per minute . , 



Simple 

Corliss at 

Creusot. 


Compound 
Mill-Engine- 


60 

84 

9 

16. Q 


127 
148 

20 

II. 8 
220 



Triple 

Leavitt at 

Chestnut 

Hill. 



50.6 
176 

21 

II. 2 
204 



Gain from compounding, 

16.9 — 11.^ 



16.9 



0.30. 



Gain from using triple engine in place of simple engine, 
16.9 — II. 2 _ 



16.9 



0.34. 



Gain from using triple engine in place of compound engine 
II. 8 — II. 2 



11.8 



= 0.05. 



26o 



ECONOMY OF STEAM-ENGINES 



Compound and triple engines have been found well adapted 
to marine work, where for various reasons a short cut-off cannot 
well be used. Taking the engines of the three ships mentioned 
in the following supplementary table to represent good practice, 
we can determine the gain from compounding. 



Data and Results. 



Revolutions per minute ..... 

Steam pressure by gauge 

Total expansion 

Steam per horse-power per hour, pounds 



Simple 


Compound 


Galatin. 


Rush. 


5t 


n 


65 


69 


4.5 


6.2 


22 


18.4 



Triple 
Meteor. 



72 

145 
ro.6 

IS 



Gain from compounding, 



22 



18.4 



= 0.16. 



22 



Gain from using triple engine instead of simple engine, 



22 — iq 

22 ^ 



Gain from using triple engine instead of compound engine, 



i8-4 - 15 
18.4 



= 0.18. 



Two things are to be noted: first, that the total number of 
expansions is very moderate even for the triple engine; and, 
second, that the steam-consumption is correspondingly large 
as compared with that for stationary engines. 

A notable exception in marine practice is the engine of the 
lona^ which was relatively much larger than can commonly be 
placed in a steamer; it had the advantage of 165 pounds steam- 
pressure and 19 total expansions, and had a steam-consumption 
of only 13 pounds per horse- power per hour. 



EXPERIMENTAL ENGINE 261 

Properly the comparison for finding the gain from compound- 
ing should be based on thermal units per horse-power per minute, 
but the data for such a comparison are not given for all the 
engines, and as all the engines have steam-jackets, the comparison 
of steam-consumptions is not much in error. 

Steam-jackets. — As has already been pointed out in the 
discussion of the influence of the cylinder walls, the beneficial 
action of a steam-jacket is to dry out the cylinder during exhaust, 
without unduly reducing the temperature of the cylinder walls, 
and thus check the condensation during admission. The steam- 
jacket does indeed supply some heat during expansion, but 
that effect is of secondary importance, and the heat is applied 
with a thermodynamic disadvantage. The principal effect is 
thus to supply heat which is thrown out in the exhaust, which is 
all lost in case of a simple engine; in case of a compound engine 
the heat supplied by a jacket during exhaust from the high- 
pressure cylinder is intercepted by the low-pressure cylinder, 
and is not entirely lost. It would clearly be much more advan- 
tageous to make the cylinders of non-conducting material, if 
that were possible. A clear grasp of the true action of the 
steam-jacket has a natural tendency to prejudice the mind 
against that device, and this prejudice has in many cases been 
strengthened by the confusion that has come from indiscriminate 
comparison of many tests made to determine the advantage 
from the use of steam-jackets. 

There are two series of tests that appear to dispose of this 
question, — those by Delafond on the Corliss engine at Creusot, 
and those made at the Massachusetts Institute of Technology 
on a triple-expansion experimental engine; the former has already 
been given, and the latter will now be detailed; afterward the 
gain from the use of the jacket will be discussed. 

Experimental Engine at the Massachusetts Institute of 
Technology. — This engine, which was added to the equipment 
of the laboratory of steam-engineering of the Institute in 1890, 
is specially arranged for giving instruction in making engine- tests. 
It has three horizontal cylinders and two intermediate receivers. 



262 ECONOMY OF STEAM-ENGINES 

the piping being so arranged that any cylinder may be used 



340 



aoo 



240 



220 



200 



























i 




















^ 


\ 




















\ 


^V 




















s 


N 


;/c 


3mpou 


id. 






\ 








y 


W 


ithout 


jacket 


J 




^ 


\ 




















\ 


V 
















•s 


\, 


^ 


<, 














^ 


v- 


V, 


?^ 


S 


V 


Trip 
* with 


le, 
out ja 


ikets 






\ 


/ \ 


^^ 






Tn 

r^ on 


ple,ja( 
heads 


kets 






• 


\ 


\ 


















\ 


\^ 


N^ 




Trii 
- on ( 
^ and 


le,jacl 
ylinde 
receiv 


ets 










• 




< 


^on c 


iple,ja 
jrlinde 


3kets 
s only 












n 



















































10 



20 



30 



40 



Fig. 59 



singly or may be combined with one or both of the other cylinders 
to form a compound or a triple engine. Each cylinder has 



EXPERIMENTAL ENGINE 263 

Steam-jackets on the tarrel and the heads, and steam may be 
supplied to any or all of these jackets at will. The steam con- 
densed in the jackets of any one of the cylinders is collected under 
pressure in a closed receptacle and measured. Originally the 
receivers were also provided with steam-jackets; now they are 
provided with tubular reheaters so divided that one-third, two- 
thirds, or all the surface of the reheaters can be used. The 
steam condensed in the reheaters is also collected and measured 
in a closed receptacle. 

The valve-gear is of the Corliss type with vacuum dash-pots 
which give a very sharp cut-off. The high- pressure and inter- 
mediate cylinders have only one eccentric and wrist-plate, and 
consequently cannot have a longer cut-off than half stroke under 
the control of the drop cut-off mechanism. The low-pressure 
cylinder has two eccentrics and two wrist-plates, and the admission 
valves can be set to give a cut-off beyond half stroke. The 
governor is arranged to control the valves for any or all of the 
cylinders. Each cylinder has also a hand-gear for controlling 
its valves. For experimental purposes the governor is set to 
control only the high-pressure valve-gear, when the engine is 
running compound or triple-expansion. The hand-gear is 
used for adjusting the cut-off for the other cylinder or cylinders; 
usually the cut-off for such cylinder or cylinders is set to give a 
very small drop between the cylinders. This arrangement 
throws a very small duty on the governor, so that by the aid of 
a large and heavy fly-wheel the engine can be made to give 
nearly identical indicator-diagrams for an entire test during 
which the load and the steam-pressure are kept constant. 

The main dimensions of the engine are as follows: 

Diameter of the high-pressure cylinder 9 inches. 

intermediate " 16 '' 

** *' low-pressure '' 24 " 

' ' " piston-rods 2^^ " 

Stroke 30 * ' 



264 ECONOMY OF STEAM-ENGINES 

Clearance in per cent of the piston displacements: 

High-pressure cylinder, head end, 8.83; crank end, 9.76 
Intermediate " " '' 10.4 " '' 10.9 

Low-pressure " '' "11.25 " " 8.84 

Results of tests on the engine with the cylinders arranged in 
order to form a triple-expansion engine are given in Table 
XXIII, and are represented by the diagram Fig. 60 with the 
cut-off of the high-pressure cylinder for abscissae and with the 
consumptions of thermal units per horse-power per minute as 
ordinates. 

The most important investigation which has been made on 
this engine is of the advantage to be obtained from the use of 
steam in the jackets. Four series of tests were made for this 
purpose: (i) with steam in all the jackets of the cylinders and 
receivers, (2) with steam in the jackets of the cylinders, both 
heads and barrels, (3) with steam in the jackets on the heads of 
the cylinders only, and (4) without steam in any of the jackets. 

The most economical method of running the engine was with 
steam in all the jackets on the cylinders, but without steam in 
the receiver-jackets, as shown by the lowest curve on Fig. 59. 
There is a small but distinct disadvantage from using steam in 
the receiver-jackets also. This fact could not be surely deter- 
mined from any pair of tests, for the difference is not more than 
two per cent, and is therefore not more than the probable error 
for such a pair of tests, but a comparison of the two curves on 
Fig. 59, representing tests under the two conditions, gives con- 
clusive evidencfe with regard to this point. It may not be im- 
proper in this connection to call attention to the three points 
below the lowest curve and not connected with it ; they represent 
tests which were made after the nine tests represented by points 
joined to the curve, and when some additional non-conducting 
covering had been applied to the piping and valves of the engine. 
Here the slight gain from reduced radiation is made manifest, 
though it is too small to be taken into account in making com- 
parisons of the different conditions of running the engine. 



EXPERIMENTAL ENGINE 



265 



Table XXIII. 

TRIPLE-EXPANSION EXPERIMENTAL ENGINE AT THE MASSA- 
CHUSETTS INSTITUTE OF TECHNOLOGY. 

Trans. Am. .Soc. Mech. Engs., 1892-1804; Technology Quarterly, 1896. 















Steam used in jackets, 






















per cent. 














i 
^ 


ij 
3^ 


1 


8s 


1. 








u 


S3 

k 


ll 


-S s 
eg 

Mo 




a 


! 


u 


i 


a 


1 


« 




1 
146.2 




Is 

1 




i 


is 
1" 


i 




1 



It 

SB. 

a 
.0^ 


1- oj 




1 


89-93 


36.1 


24.1 


29.8 


3-2 




8.6 


6.3 


140.8 


iv8 


240 


233 


2 a . 


90.60 


35-0 


147.0 


24-7 


30.3 


2.5 




8.8 




5.4 


138.0 


13-9 


241 


237 


3 5- 


91-93 


27-3 


146.9 


24-5 


29-9 


2-5 




8.5 




7.2 


125.4 


13.7 


237 


231 


4 ^-S 


91-55 


27.0 


146.7 


25-4 


30.1 


3.2 




9.8 




8.1 


123.9 


13.7 


239 


236 




92-37 


25.0 


146.6 


24-5 


30.7 


3-4 




10.4 




10. 1 


114-7 


14.3 


247 


240 


6 ^-^ 


84-87 


21.9 


145.2 


24-3 


30.1 


3-S 




11-3 




8.7 


ioS-3 


14.5 


250 


241 


7 ^" 


93-15 


17.4 


146.0 


26.0 


30.2 


3.5 




10.7 




II. b 


103-5 


14.7 


255 


255 


8 


86.70 


12.0 


147.0 


27.4 


.30.5 


6.1 




15.2 




12.2 


78-3 


15-1 


261 


273 


9 


87-55 


ii.3 


146.7 


26.0 


30.1 


6.5 




15-3 




13.0 


67.4 


16.0 


274 


274 


10 


84.23 


13.5 


X45.2 


26.1 


30.0 


5-3 




11-3 




12. 1 


77.8 


14.7 


253 


255 


II Ditto. 


82.50 


20.5 


144.5 


26.2 


29.9 


4.5 




9.1 




9.9 


101.9 


13.5 


235 


237 


12 


82.13 


23.6 


145.3 


26.4 


30. 1 


3.1 




8.5 




9.8 


104.2 


. ^^-s 


232 


235 


13 CT3 . 


91.20 


36.1 


143-7 


24.7 


30.2 


2.6 


4.7 


6.4 


5.4 


5.9 


154.2 


14.4 


249 


244 


14 °g^ 


91.40 


32.8 


143.6 


25-0 


30.2 


2.9 


6.4 


7-1 


4-3 


6.4 


145-1 


14.1 


244 


240 


IS ^ >« > 


91.82 


29-3 


143-2 


25-2 


30.5 


3.0 


5.6 


7.6 


4.9 


6.1 


137-0 


143 


246 


243 


16 ^-Ss 


91.83 


27-5 


147.1 


24.7 


30.3 


1.4 


4-7 


8.9 


31 


7.3 


128.8 


14.1 


242 


237 


^7 rt-r^£ 


92.17 


25-9 


145.5 


^|-^ 


30.4 


3-2 


4-5 


8.2 


4.7 


5-7 


125.8 


14. 1 


243 


241 


18 'J 


92.57 


21.9 


143.7 


26.4 


30.6 


3-4 


6.8 


7.1 


4-1 


7.7 


120.2 


14.6 


256 
290 


258 


<9 


84.95 


9-1 


145.8 


25.6 


30.0 


2.9 




7.7 




8.7 


55-9 


16.6 


285 


20 J. 


84.03 


13-9 


144.5 


26.4 


29-9 


2. 1 




7.2 




8.6 


69-4 


15.5 


273 


277 


21 ^ ^ 


83-35 


15.6 


144.9 


25.6 


29.8 


2.2 




6.8 




8.0 


72.8 


15.5 


273 


269 


22 ^-a 


82.40 


20.7 


145-3 


26.7 


30.3 


1.4 




6.6 




8.0 


84.2 


15-1 


269 


269 


=^3-^2 


81.40 


27.3 


144-2 


24.7 


29-7 


1.3 




7-7 




5.6 


97-4 


15-2 


267 


261 


24 ^~ 


81.05 


29.7 


143-4 


25.4 


29.9 


1.4 




5.3 




6.8 


101.5 


15.0 


265 


263 


25 ■"" 


80.28 


34.9 


143- 1 


25.5 


30.2 


1.2 




5.0 




6.4 


109.4 


15-0 


26 s 


262 


26 


80.32 


35.6 


144.0 


25.0 


29.9 


1 . 1 




4.6 




7-4 


114.1 


15-2 


267 


264 


27 


85.60 


8.4 


152.8 


26.1 


29.7 












53-2 


17.3 


318 


318 


28 


85.62 
85.60 
84.22 


8-3 
10.6 
iv8 


153-3 
152-1 
152.8 


26.1 

26.1 

259 














55-7 
60.6 
74-9 


16.9 
16.2 

15-4 


306 
296 
287 


C508 


29 


29.9 
29.8 












297 


<o 












286 


31 


83 C3 


21.3 


152.0 


26., 














85-8 


15. I 


276 


277 


32 ./ 


82.92 


21.2 


152.4 


26.09 


30.15 










86.9 


15.4 


281 


281 


33 "S 


82.55 
83.32 
82.67 
81.78 
82.92 
81.52 
81.57 
81.40 
81.50 


21.0 
24.1 

29.5 
29.1 
28.7 
30.7 
31.8 
35.6 
33-8 


1530 
152.0 
151-9 
152-0 
152. 5 
151. 5 
152.0 
152-0 
151.9 


26.02 

25-70 

25-6 

26.0 

26.1 

26.0 

26.04 

25-9 


30.0 


1 








87.8 
91.1 
99-9 
100.5 
102.4 
106.0 
108.2 
III. 2 
112. 2 


15-2 
15-5 
15-5 
15-2 
15-0 

15-2 

14-9 
14-3 
151 


284 
280 
283 
275 
272 
278 
271 
274 
274 


?8^ 


34 "i 












,278 


35 •" 


30.0 












?8o 


37 ^ 












273 


29.9 
29.9 














38 












278 


39 














40 


30.1 
30.26 












274 


41 












i274 










, 





266 



ECONOMY OF STEAM-ENGINES 



Table XXIV gives tests made on this engine without steam 
in the jackets and with steam suppUed to the tubular reheaters; 
the results of these tests will be discussed later. 



Table XXIV. 

TRIPLE-EXPANSION EXPERIMENTAL ENGINE AT THE MASSA- 
CHUSETTS INSTITUTE OF TECHNOLOGY WITH TUBULAR 
REHEATERS. 





Condition. 


I 

It 
1^ 


li 


la 


§1. 

.S-Sg 

ill 


n 


Per cent of 
steam used 
in reheaters. 


w 




0^ 

Hi 






i 


n3 




I 


Without 
steam in 
reheaters. 


8i.8 
8i.8 
8i.6 

8l.2 


27 
27 
29 
36 


146.7 

147-5 
I47-0 
148.2 


26.4 
26.1 
25-9 
25-9 


30.6 
30.4 
30.5 
30.2 






88.6 

87-5 

89.7 

103-3 


16.0 
16.0 
16.0 

15. 5 


290 
291 
290 
282 


288 
28 






3 
4 






28 
281 












5 
6 

7 


Steam in 

first 
reheater. 


85. S 
83.5 
81.4 


10 
31 


147-2 
146.9 
146. 1 


25-5 
23.8 
25.8 


30.0 
30.2 
30.2 




13 
14 
12 


66.5 

84.9 
112. 4 


15-7 
15.9 
15.0 


277 
277 
266 


273 
262 
264 


8 
9 

lO 

II 

12 


Steam in 

both 
reheaters. 


85.0 
84.5 
82.4 
8i.9 
82.0 


8 
10 
21 
27 
28 


147-3 
146.9 
147. 1 
147.7 
146.6 


26.6 
26.2 
25.3 
25-4 
25-7 


30.3 
30.3 
30.4 
30.1 
30.2 


10 
12 
10 
6 

7 


7 
8 
6 
9 
8 


61.5 

74.8 

95-7 

105.9 

107.0 


15-5 
14.9 
14.7 
14.7 
X4.5 


269 
261 
258 
259 
256 


274 
260 
252 
254 
254 



Gain from Steam-jackets. — Much of the difference of opinion 
concerning the advantage to be derived from the use of steam- 
jackets is to be ascribed to indiscriminate comparison of tests 
on various engines, or to the failure to obtain any advantage 
from jackets which were not applied with discrimination. Should 
any engine when properly tested and computed, show no advan- 
tage from the use of a steam-jacket, it will be better to omit 
that device in future constructions for the same conditions 
unless there are constructive reasons for retaining it. 

In order to obtain definite conclusions from tests made to 
determine the advantage of the use of steam-jackets, such tests 
should be made in definite series in which only one property is 
varied at a time, and from these tests the best results under 



GAIN FROM STEAM-JACKETS 267 

the most favorable conditions should be chosen when the engine 
has steam in the jackets, and in like manner the best result 
without steam in the jackets should be selected; a comparison 
of two such selected tests has more weight than a haphazard 
comparison of individual tests, however great the number of 
such tests may be. An investigation of Delafond's tests in 
Tables XXI and XXII and represented by Figs. 57 and 58, 
gives such a comparison. The tests selected are those given in 
Table X and give two pairs, with condensation and without. 
Thus the best result with steam in the jacket and with conden- 
sation is 16.9 pounds, and without steam in the jacket is 18. i; 
the gain is 

18. 1 — 16. Q 

=0.07. 

18. I ' 

Without condensation the best results are 21.5 with steam in 
the jackets and 24.2 without steam in the jackets; the gain is 

24.2 — 2\X 

-^ -^ = O.I I. 

24.2 

These results are probably too small, as the steam used in the 
jackets should be collected and returned to the boiler with only 
a moderate reduction of temperature below the temperature of 
the steam in the boiler. The drip from the jackets was passed 
through a trap, and as reported is probably too small, this being 
the most questionable result from the tests. 

Data for a similar comparison for compound engines are not 
at hand, but the tests described on page 265 seem to be conclusive 
for the triple engine. 

From the diagram Fig. 59 the best results with steam in all 
the jackets of the cylinders and without steam in, any of the 
jackets are 233 and 274 b.t.u. per horse-power per minute, and 
the gain from the use of the steam in the jacket is 

274 — 2'\'\ 

-^ "^^ X 100 = IS per cent. 

274 



268 ECONOMY OF STEAM-ENGINES 

These heat-consumptions correspond to 13.8 and 15.2 pounds 
of steam per horse-power per hour, so that on the basis of steam- 
consumption the gain from the use of steam in the jackets would 
appear to be only 9 per cent, instead of the actual gain of 15 per 
cent. This large difiference is due to the large percentage of 
steam used in the jackets, amounting in all to 17 or 18 per cent 
of the total steam-consumption. The steam used in an indi- 
vidual jacket is, however, not excessive, being about 2.5 per cent 
in the jackets of the high- pressure cylinder and 7 or 8 per cent in 
the jackets of each of the other two cylinders. 

The effect of jacketing the heads of the cylinders only is 
surprisingly small, as from the diagram the best result is 262 
B.T.u. per ^horse-power per minute, which compared with the 
best result without steam in any of the jackets gives a gain of 
only 

274 — 262 

~ X 100 = 4 per cent. 

274 

The correspondence between this result and the experiments by 
Callendar and Nicolson on the action of the cylinder walls, 
has already been pointed out. 

From the tests just discussed and compared it appears con- 
servative to say that about ten per cent can be gained by using 
steam-jackets on simple and compound engines and that fifteen 
per cent can be gained by their use on triple-expansion engines; 
provided that these conclusions shall not be applied to engines of 
more than 300 horse-power. The saving on massive engines 
of 1000 horse-power or more is likely to be smaller, and very 
large engines may derive no benefit from steam-jackets. On 
the other hand, a saving of 25 per cent may be obtained from 
jackets on small engines of five or ten horse-power. Such trivial 
engines are never provided with jackets unless for experimental 
purposes, and the results of such experiments are of little value. 

Intermediate Reheaters. — Many compound and triple- 
expansion engines have some method of reheating the steam 
on its way from one cylinder to another. Notable examples 



INTERMEDIATE REHEATERS 269 

are the Leavitt pumping-engines, for which results are given in 
Table X. The fact that these engines give the best economies 
recorded for engines using saturated steam lead to the inference 
that such reheaters may be used to advantage. The only direct 
evidence, however, is not so favorable, for, as has been pointed 
out on page 264, there was found a small but distinct disadvantage 
from using steam in double walls or jackets on the intermediate 
receivers of the experimental engine at the Massachusetts Institute 
of Technology. It appears that this engine gives the best 
economy when steam is supplied to the jackets on the cylinders 
and not to the jackets on the reheaters, and, further, that when 
steam is used in the receiver-jackets the steam in the low- 
pressure cylinder shows signs of superheating, which may be 
considered to indicate that the use of the steam-jacket is carried 
too far. 

After the tests referred to were finished the engine was fur- 
nished with reheaters made of corrugated-copper tubing, so 
arranged that one-third, two-thirds, or all of the reheating-surface 
can be used, when desired. Table XXIV, page 266, gives the 
results of tests made on the engine with and without steam in 
the reheaters; in these tests the entire reheating-surface was used 
when steam was supplied to a reheater. 

For some reason the heat-consumption when no steam was 
used in the reheaters is somewhat greater than that given in 
Table XXIV for the engine without steam in any of the 
jackets; the difference, however, is not more than two or two 
and a half per cent and cannot be considered of much importance. 
It is clear from the table that there is advantage from using one 
reheater, and still more from using two. If the heat-consumption 
for the engine without steam in the jackets and without steam 
in the reheaters (taken from Table XXIV) is assumed to be 
274 B.T.u. per minute, then the gain from using the reheaters 
appears to be 



274 — 2^2 „ 

-^-^ ^— X 100 == 8 per cent, 

274 



270 ECONOMY OF STEAM-ENGINES 

which is scarcely more than half the gain from using steam in 
the jackets. These tests cannot be considered conclusive, as 
they are too few and refer only to one engine. 

Superheating. — The most direct and effective way of reducing 
the interference of the cylinder walls and of improving steam- 
engine economy is by the use of superheated steam. About 
1863-64 a number of naval vessels were supplied with super- 
heaters by Chief Engineer Isherwood, and when tested by him 
showed a marked advantage which led to the adoption of super- 
heated steam for stationary and marine practice both in America 
and in Europe. But the superheaters which were exposed to 
dry steam on one side and to the flue gases on the other, rapidly 
deteriorated, and after an experience lasting ten or fifteen years 
the use of superheated steam was abandoned in favor of com- 
pound and triple engines with high-pressure steam. 

More recently improved forms of superheaters have been 
introduced in Great Britain and Germany, which show good 
endurance, and superheated steam appears to have been used 
successfully for sufficient times to warrant the conclusion that 
the application of superheated steam has been accomplished. 
Two series of tests will be discussed, namely, some early tests 
on a simple engine, and some recent tests on compound engines. 
There appears to be no reason for extending the application of 
superheated steam to triple engines. 

Dixwell's Tests. — A small Harris- Corliss engine was fitted 
up for making tests on superheated steam at the Massachusetts 
Institute of Technology by Mr. George B. Dixwell. Six tests 
with superheated and saturated steam were made on this engine 
in 1877 in the presence of a board of engineers of the United 
States Navy. 



DIX WELL'S TESTS 



271 



Table XXV. 

DIXWELL'S TESTS ON SUPERHEATED STEAM. 

CYLINDER DIAMETER 8 INCHES; STROKE 2 FEET. 

Proceedings 0} the Society of Arts, Mass. Inst. Tech., 1887-88. 



Diiration, minutes 

Cut-off 

Revolutions per minute 

Boiler-pressure above atmosphere, pounds 

per square inch 

Back-pressure, absolute, pounds per sq. in 
Temperatures Fahrenheit: 

Near engine 

In cylinder by pyrometer 

Per cent of water in cvlinder : 

At cut-off 

At end of stroke 

Horse-power 

Steam per horse-power per hour, poimds, 
B.T.U. per horse- power per minute. . . 



Saturated Steam. 


Superheated St 


I 


II 


III 


IV 


V 


127 


83 


63 


180 


108 


0.217 


0.443 


0.689 


0.218 


0.439 


61. s 


60.4 


58.0 


61 .0 


61.4 


50.4 


SO. 2 


50.3 


50.4 


50.0 


15-4 


15-7 


15.8 


15-2 


15-4 


302 


303 


303 


478 


441 


278-297 


279-296 


282—300 


313 


316 


52. 2 


35-9 


27.9 


27.4 


13-6 


32.4 


293 


23-9 


18.3 


13.6 


7.65 


12.7 


15.68 


6.83 


12.37 


48.2 


42.2 


45-3 


35-2 


31-7 


796 


696 


747 


631 


546 



VI 



75 
0.672 
59-5 

SO. 2 
15-5 

406 
315 

8.9 

II. 5 

15-63 

35-8 

621 



A metallic thermometer or pyrometer was placed in a recess 
in the head of the cylinder. When saturated steam was used 
this pyrometer showed a large fluctuation, but when superheated 
steam was used its needle or indicator was at rest. Even if a 
part of the apparent change of temperature with saturated steam 
is attributed to the vibration of the needle and the multiplying 
mechanism, it is very clear that the use of superheated steam 
reduces the change of temperature of the cylinder-head in a 
remarkable manner. The effect of superheating on the action 
of the cylinder walls is also indicated by the per cent of water 
in the cylinder at cut-off and release. 

The apparent gain by comparing the amounts of steam used 
per horse-power per hour in favor of superheated steam is but 



42.2 - 31.7 
42.2 



X 100 = 25 per cent; 



this result is of course misleading, since the superheating required 
additional coal. As the coal-consumption was not determined, 



272 ECONOMY OF STEAM-ENGINES 

we must compare instead the b.t.u. per horse-power per minute, 
giving a real gain of 

696 — 546 ^^ 

-^ — — ~ — X 100 =19 per cent. 
696 

This same Harris- Corliss engine afterwards showed a heat- 
consumption of 548 B.T.U. per horse-power per minute when 
supplied with saturated steam at 77 pounds pressure, which shows 
why the earlier attempts at the use of superheated steam were 
so easily set aside when it was found expedient to raise the steam- 
pressure. 

Though we have no tests with high-pressure steam and with 
condensation on engines of two or three hundred horse- power, 
it is probable that a very material saving could be made by the 
use of superheated steam under such conditions ; if the saving in 
heat were as much as fifteen per cent, it would reduce the steam- 
consumption to a larger degree, perhaps by twenty per cent, 
and would be likely to give from 14.5 to 15 pounds of superheated 
steam per horse-power per hour. 

The best results obtained from the application of superheated 
steam in compound engines are reported by Professor Schroter, 
in Table XXVI, for a tandem-engine with poppet-valves 
built in Ghent. Five tests were made with varying cut-off and 
with saturated steam, and five others also with varying cut-off 
and with steam that was superheated about 250° F., the absolute 
initial pressure in the cylinder being about 145 pounds, so that 
the boiler- pressure was probably between 130 and 135 pounds by 
the gauge. 

This engine gave a remarkable economy both with saturated 
steam and with superheated steam, its steam and heat-consump- 
tion being only five per cent more than that of the triple-expansion 
Leavitt engine recorded in Table X. The gain from using 
superheated steam appears to be 

213 - 199 

^^— o.oO, 

213 



SCHROTER TESTS 



273 



which places it a little beyond the performance of the triple 
engine mentioned. But since the uncertainty of the determina- 
tion of power by the indicator is probably two per cent, we may 
reasonably conclude that the effect of using superheated steam 
in a compound engine is to place it on a level with a triple 
engine, and the question is to be decided in practice by the 
relative expense and trouble of supplying and using a superheater 
instead of a third cylinder and higher steam-pressure. 

It is somewhat remarkable that steam was supplied to the 
jackets during the superheating tests, but not at all surpris- 
ing that for those tests the jackets had a small effect, as is 
made evident by noting the percentages of steam condensed in 
them. 

Table XXVI. 

COMPOUND HORIZONTAL MILL-ENGINE. 

CYLINDER DIAMETERS 12.8 AND 22 INCHES; STROKE 33.5 INCHES. 

By Professor M. Schroter, Mitleilungen iiher Forschungsarheiten, 
Heft 19, 1904. 



Horse-power 

Duration, minutes 

Revolutions per minute . . 
Cut-off, high-pressure cylinder 

Total expansions 

Initial pressure, absolute pounds per 

so. in 
Back-pressure, absolute pounds per 

sq . in 



Superheating, degrees F 

Steam per horse-power per hour, 

pounds 

Per cent condensed in jackets . 
B.T.U. per horse-power per min. 
Mechanical efficiency .... 



Saturated . 



299 

60 

126 

0.38 

7-9 

148 



13-6 

10.9 

246 

>.90i 



II III IV V 



263 

61 

126 

0.31 

9-7 

146 



12.8 

II. 8 

232 

).89i 



211 

57-5 

126.5 

0.22 

13-5 

147 



12.3 

12.9 

222 

).872 



160 
55 

127 

0.15 

20 



13-7 

213 

3.842 



50 

128 

o.io 

30 



14.4 

216 

).786 



Superheated. 



VI VII VIII IX X 



303 

48 

126 

0.41 

7-3 

T48 

1-3 
246 

10.9 

2.1 

223 

3.902 



258 

60 

126 

0.33 

9.1 

149 

i.o 

257 



3-5 

215 

0.890 



112 

51 

126. 5 

0.26 

ii-S 

149 

1. 1 
258 



3» 

206 

0.872 



161 
64- 5 

127 
o. 16 
18.7 

146 



256 

9-7 
4.4 
201 
.842 



o. 10 

30 



.46 



256 

9.6' 

4.6 

199 

0.790 



Cut-off and Expansion. — It has already been pointed out on 
page 256 in connection with Delafond's tests that the best point 
of cut-off for a simple engine, whether jacketed or not, is about 



274 ECONOMY OF STEAM-ENGINES 

one-third stroke when the engine is non-condensing, and it is 
about one-sixth stroke when condensing. In general, other 
tests on simple engines such as those on the Gallatin, and on 
the small Corliss engine at the Massachusetts Institute of 
Technology, confirm these conclusions. 

The term total expansion for a compound or a triple engine 
can properly have only a conventional significance; it is usually 
taken to be the product of the ratio of the large to the small 
cylinder by the reciprocal of the fraction of the stroke at cut-off 
for the high-pressure cylinder. This conventional total expan- 
sion is about 20 for all the tests on triple engines quoted in Table 
X, except those on marine engines, w^hich show a relatively 
poor economy. It may therefore be concluded that it is not 
advisable to use much more expansion for any triple engine, 
and that less expansion should be used only when the condi- 
tions of service (for example, at sea) prevent the use of large 
expansion. 

The stationary compound engines given in Table X also 
have about 20 expansions, and experience shows conclusively 
that highest economy for such a degree of expansion is re- 
quired. In practice somewhat less may frequently be found 
advisable. 

Variation of Load. — In general, an engine should be so 
designed that it may give a fair economy for a considerable 
range of load or power. Very commonly the engine will have 
sufficient range of power with good economy if designed to give 
the best economy at the normal load. In general, however, 
it is well to assign a less expansion and consequently a longer 
cut-off to the engine than would be determined from a con- 
sideration of the steam- (or heat-) consumption alone. For, 
in the first place, the best brake or dynamic economy is always 
attained for a little longer cut-off than that which gives the 
best indicated economy, and in the second place the economy 
is less affected by lengthening than by shortening the cut-off. 
The first comes from the fact that the frictional losses of the 
engine increase less rapidly than the power, as will be shown 



VARIATION OF LOAD 



275 



in the next chapter; and the second is evident from consideration 
of curves of steam-consumption as given by Fig. 59, page 262, 
and Figs. 57 and 58, pages 252-253. 

The allowable range of power for a simple engine is greater 
than for a compound or a triple engine. Comparisons for a 
simple and a triple engine may be made by aid of Figs. 58 and 
59. The Corliss engine at Creusot when supplied with steam 
at 60 pounds pressure, with condensation and with steam in 
the jacket, developed 150 horse-power and used 17.3 pounds 
of steam per horse-power per hour. If the increase be limited 
to 10 per cent of the best economy, that is, to 19 pounds per 
horse-power per hour, the horse-power may be reduced to about 
92, giving a reduction of nearly 40 per cent from the normal 
power. The triple engine at the Massachusetts Institute of 
Technology with steam at 150 pounds pressure and using steam 
in all the cylinder- jackets developed 140 horse-power and used 
233 B.T.u. per horse-power per minute. Again, limiting the 
increased consumption to ic per cent or to 254 b.t.u., the power 
may be reduced to about 104 horse-power, giving a reduction of 
26 per cent from the normal power. The effect of increasing 
power for these engines cannot be well shown from the tests 
made on them, but there is reason to believe that the simple 
engine would preserve its advantage if a comparison could be 
made. Though the tests which we have on compound engines 
do not allow us to make a similar investigation of the effect of 
changing load, there is no doubt that it is intermediate in this 
respect between the simple and the triple engine. 

When the power developed by a compound engine is reduced 
by shortening the cut-off of the high-pressure cylinder, the cut-off 
of the low-pressure cylinder must be shortened at the same time 
to preserve a proper distribution of power and division of the 
range of temperature between the cylinders. If this is not done 
the work will be developed mainly in the high-pressure cylinder, 
which will be subjected to a large fluctuation of temperature, 
and the engine will lose the advantages sought from compounding. 
A compound non-condensing engine, if the cut-off for the large 



276 ECONOMY OF STEAM-ENGINES 

cylinder is fixed, is likely to have a loop on the low-pressure 
indicator-diagram due to expansion below the atmosphere, if 
the power is reduced by shortening the cut-off of the high-pressure 
cylinder. Such a loop is always accompanied by a large loss of 
economy; if the loop is large the engine may be more wasteful 
than a simple engine, for the high-pressure piston develops 
nearly all the power and may have to drag the low-pressure 
piston, which is then worse than useless. 

There is seldom much difficulty in running a simple engine at 
any desired reduced power by shortening the cut-off or reducing 
the steam-pressure, or by a combination of the two methods. 
But a compound engine sometimes gives trouble when run at 
very low power (even when attention is given to the cut-off of 
the low-pressure cylinder), which usually takes the form just 
discussed ; i.e., the power is developed mainly in the high- pressure 
cylinder. Triple engines are even more troublesome in this 
way. A compound or triple engine running at much reduced 
power is subject not only to loss of economy and to irregular 
action, but the inside surface of the low-pressure cylinder is 
liable to be cut or abraded. 

Automatic and Throttle Engines. — The power of an engine 
may be regulated by (i) controlling the steam- pressure, or (2) 
by adjusting the cut-off. Usually these two methods are used 
separately, but in some instances they are used in combination. 
Thus a locomotive-driver may reduce the power of his engine 
either by shortening the cut-off or by partially closing the throttle- 
valve, or he may do both at once. Stationary engines are usually 
run at a fixed speed and are controlled by mechanical governors, 
which commonly consist of revolving weights that are urged 
away from the axis of revolution by centrifugal force and are 
restrained by the attraction of gravity or by the tension of 
springs. 

The earliest and simplest steam-engine governor, invented by 
Watt, has a pair of revolving pendulums (balls on the ends of 
rods that are hinged to a vertical spindle at their upper ends) 
which arc urged out by centrifugal force and are drawn down 



AUTOMATIC AND THROTTLE ENGINES 



277 



by gravity. When the engine is running steadily at a given 
speed the forces acting on the governor are in equiUbrium and 
the balls revolve in a certain horizontal plane. If the load on 
the engine is reduced the engine speeds up and the balls move 
outward and upward until a new position of equilibrium is 
found with the balls revolving in a higher horizontal plane. 
Through a proper system of links and levers the upward motion 
of the balls is made to partially close a throttle- valve in the pipe 
which supplies steam to the engine and thus adjusts the work of 
the engine to the load. 

Shaft-governors have large revolving- weights whose centrifugal 
forces are balanced by strong springs. They are powerful 
enough to control the distribution or the cut-off valve of the 
engine, which, however, must be balanced so that it may move 
easily. 

Automatic engines, like the Corliss engines, have four valves, 
two for admission and two for exhaust of steam. The admission, 
release, and compression are fixed, but the cut-off is controlled 
by the governor. Usually an admission- valve is attached to the 
actuating mechanism by a latch or similar device, which can be 
opened by the governor, and then the valve is closed by gravity 
by a spring, or by some other independent device. The office 
of the governor is to control the position of a stop against 
which the latch strikes and by which it is opened to release the 
valve. 

Corliss and other automatic engines have long had a deserved 
reputation for economy, which is commonly attributed to their 
method of regulation. It is true that the valve-gears of such 
engines are adapted to give an early cut-off, which is one of the 
elements of the design of an economical simple engine, but their 
advantage over some other engines is to be largely attributed 
to the small clearance which the use of four valves makes con- 
venient, and to the fact that the exhaust-steam is led immediately 
away from the engine, without having a chance to abstract heat 
after it leaves the cylinder. These engines also are free from 
the loss which Callendar and Nicolson attribute to direct leakage 



278 ECONOMY OF STEAM-ENGINES 

from the steam to the exhaust side of slide-valves, and to valves 
of similar construction. 

Every steam-engine should have a reserve of power in excess 
of its normal power; and again it is convenient if not essential 
that a single-cylinder engine should be able to carry steam 
through the greater part of its stroke in starting. These condi- 
tions, together with the fact that it is somewhat difficult to design 
a plain slide-valve engine to give an early cut-off, have led to the 
use of a long cut-off for engines controlled by a throttle-governor. 
The tests on the Corliss engine at Creusot (Tables XXI and 
XXII, pp. 250 and 251) show clearly the disadvantage of using 
a long cut-off for simple engines. It has already been pointed 
out that a non-condensing engine should have the cut-off at 
about one-third stroke. With cut-off at that point and with 75 
pounds steam- pressure the engine developed 209 horse-power 
and used 24.2 pounds of steam per horse-power per hour when 
running without steam in the jacket and without condensation.- 
If the steam-pressure is reduced to 50 pounds and the cut-off is 
lengthened to 58 per cent of the stroke, the steam-consumption 
is increased to 30.2 pounds per horse-power per hour, the horse- 
power being then 173. The gain from using the shorter cut- 
off is 

^0.2 — 24.2 ^, ^ . 

X 100 = 20 per cent. 

30.2 

A similar comparison for the same engine running with a 
vacuum and with steam in the jacket shows even a larger differ- 
ence. Thus in test 16 the steam- pressure is 84 pounds and the 
cut-off is at 1 1.5 per cent of the stroke, the horse-power is 176, 
and the steam-consumption per horse-power per hour is 16.9 
pounds, while the consumption for about the same power in test 
44 is 25.4 pounds of steam per horse-power per hour, the steam- 
pressure being 35 and the cut-off at 58 per cent of the stroke; 
here the gain from using the shorter cut-off is 

21^.4 — 16.0 ^^ 

-"^-^ X 100 = 33 per cent. 

25.4 



EFFECT OF SPEED OF REVOLUTION 279 

Considering also that automatic engines are usually well 
built and carefully attended to, while throttling-engines are 
often cheaply built and neglected, the good reputation of 
the one and the bad reputation of the other are easily ac- 
counted for. 

It is, however, far from certain that an automatic engine will 
have a decided advantage over a throttle-engine, provided the 
latter is skilfully designed, well built and cared for, and arranged 
to run at the proper cut-off. Considering the rapid increase in 
steam-consumption per horse-power per hour when the cut-off 
is unduly shortened, it is not unreasonable to expect as good if 
not better results from a simple throttling-engine than from an 
automatic engine when both are run for a large part of the time 
at reduced power. 

The disadvantage of running a compound or a triple engine 
with too little expansion can be seen by comparing the steam- 
consumptions of marine and stationary engines; on the other 
hand, the great disadvantage of too much expansion is made 
evident from the tests on the engine in the laboratory of the 
Massachusetts Institute of Technology (Table XXIII, page 
265). Considering that the allowable variation from the most 
economical cut-off is more limited for a compound or a triple 
engine, it appears that there is less reason for using an automatic 
governor instead of a throttling governor for compound and 
triple engines than there is with simple engines. Nevertheless 
the most economical engines (simple, compound, or triple) are 
automatic engines. 

Effect of Speed of Revolution. — Though the condensation of 
steam on the walls of the cylinder of a steam-engine is very 
rapid, it is not instantaneous. It would therefore appear that 
an improvement in economy might be attained by increasing the 
number of revolutions per minute; but whatever might be thus 
gained is more than offset by the increase of the dimensions of 
valves, passages, and clearances that would accompany such a 
change in speed, for it has already been pointed out that the evil 
of initial condensation is much aggravated by increasing the 



28o - ECONOMY OF STEAM-ENGINES 

surfaces exposed to steam in clearance spaces. As a matter of 
fact, all engines which for various reasons have been designed 
to run at very high rotative speeds have shown relatively poor 
economy, in part from the reason given, and in part from the 
fact that piston- valves are commonly used, and they are subject 
to the kind of leakage described by Callendar and Nicolson on 
page 234, even when they are in good condition. Very com- 
monly the engine has a fly-wheel governor, which requires the 
valve to be very free with the chance of excessive leakage. Mr. 
Willans invented a single-acting triple-expansion engine to run 
at high rotative speed, and succeeded in getting abundant steam- 
passages without excessive clearances by using a hollow piston- 
rod to carry the steam from cylinder to cylinder, all arranged 
tandem. Tests on this engine (which are not quoted elsewhere 
in this book) showed that an increase from 100 revolutions to 
200 revolutions per minute reduced the steam-consumption 
from 24.7 to 23.1 pounds per horse-power per hour, and a 
further increase of speed to 400 revolutions gave a reduction 
to 21.4 pounds; the engine was then running compound non- 
condensing. This engine used 12.7 pounds of steam per horse- 
power per hour, when developing 30 horse-power, at 380 revo- 
lutions per minute under 170 pounds gauge-pressure, acting as 
a triple-expansion condensing engine. 

Binary Engine. — On page 180, under the subject '' Compound 
Engines," attention was called to the possibility of extending the 
range of temperature for vapor-engines by the use of two fluids; 
the second fluid (for example, sulphur dioxide) being chosen so 
that a good working back-pressure could be maintained at the 
temperature of the available condensing water which acts as 
the refrigerator for the combined engines. Considering only 
the efficiency of Carnot's cycle for the customary range of 
temperature for a steam-engine, and the efficiency for the 
extended range, it appeared that a gain of 26 per cent might 
be possible. 

Recent investigations by Professor Josse on an experimental 
engine in the laboratory of the Technical High School at Char- 



BINARY ENGINE 281 

lottenburg give some insight into the possibilities of this method. 
The engine is of moderate size, developing about 150 horse-power 
as a steam-engine, and about 200 horse-power as a binary engine, 
using steam at about 160 pounds by the gauge with 200° F., 
superheating. The engine is a three-cylinder triple- expansion 
engine, but can be run also as a compound engine, though it 
probably is not proportioned to give the best economy under the 
latter condition. 

The general arrangement of the engine is as follows : the three 
steam-cylinders are arranged horizontally side by side, and the 
additional cylinder using the volatile fluid (sulphur dioxide) lies 
on the opposite side of the crank-shaft, to which it is connected by 
its own crank and connecting-rod. Steam is supplied from the 
boiler and superheater to the steam-engine, and is exhausted 
into a tubular condenser which acts as the sulphur dioxide 
vaporizes ; the condensed steam is pumped back into the boiler, 
and the vacuum is maintained by an air-pump as usual; a vacuum 
of 20 to 25 inches of mercury was maintained in this condenser. 
The vaporous sulphur dioxide at a pressure of 120 to 180 pounds 
by the gauge was led to the proper cylinder, from which it was 
exhausted at about 35 pounds by the gauge; this exhaust was 
condensed in a tubular condenser by circulating water with a 
temperature of about 50° F. at the inlet and about 65° F. at 
the exit. 

The drips from the steam-jackets of the steam-cylinders were 
piped to the steam-condenser instead of being returned to the 
boiler, but that cannot be of much importance because the 
condensation in the jackets was probably less than five per cent 
of the total steam supplied to the engine. The performance of 
the engine is given in Table XXVIII in terms of steam per 
horse-power per hour and in thermal units per horse-power per 
minute; the latter I have calculated from the total heat of the 
steam including the superheat, and the heat of the liquid at 
the vacuum in the steam-condenser. Comparisons must be 
made in terms of thermal units in order to take account of 
the superheating. 



282 



ECONOMY OF STEAM-ENGINES 



Table XXVII . 

BINARY ENGINE, STEAM AND SULPHUR DIOXIDE. 
By Professor E. JosSE, Royal Technical High School, Charlottenburg. 



Revolutions per minute . . . , 

Steam-Engine: 

Pressure at inlet, h.p. cylinder 

by gauge pounds 

Vacuum, inches of mercury . . . 
Superheating, degrees Fahrenheit 

Horse-power, indicated 

Steam p^r h.p. per hour, pounds . 
Thermal units per h.p. per minute 
Sulphur- Dioxide Engine : 

Pressure by gauge poimds: . . . 

In vaporizer 

In condenser 

Temperature Fahr. at inlet to cyl- 
inder 

Temperature Fahr. at outlet from 

condenser 

of circulating water inlet . . . 
outlet . . . 

Horse-power, indicated 

per cent of steam-engine power 
Combined Engine: 

Horse-power, indicated 

Steam per h.p. per hour, pounds . 
Thermal units per h.p. per minute 
Mechanical eflSciency 



Triple Expansion. 



39.6 



136.5 

23 -9 

17s 

132. 1 

12.5 

244 



132 
31 

132.0 

66.2 
49-6 
59-9 

45-3 
34-4 

177-4 

9-7 

183 

85.5 



136.3 



156.5 

24.1 

219 

125.2 

II. 2 

223 



128 
34 

133-7 

65.8 
49.9 
60.2 
42.8 
34-2 

168 
8.36 

167 
86.2 



143 5 



158 
20.9 

221 

154-2 

12.2 

240 



172 
35 

151. 7 

67.6 
49-9 
62.4 
56.8 
37-0 

211 
8.92 

176 
83.8 



137-4 



156.5 

25-4 

214 

101.6 

14.4 

289 



III 
31 

123-7 

64.4 
50.2 
60.2 
31.0 
30.3 

132.6 

11.05 

215 

87.5 



145 



156.5 

23.8 

210 

145-3 

13-6 

270 



142 
36 

137-3 

68.5 
50.2 
63.8 
50.1 
34-5 

195-4 

10. 12 

200 

89.1 



156-5 

20.6 

210 

144-5 

13-8 

270 



36 
157. 1 

67.6 
50.2 
63.8 
57.6 
40.0 

202. 1 

9.86 

193 

87 



148 



156.5 

20.5 

221 

161. o 

13.2 

261 



186 
36 

155- 1 

68.0 
50.2 
63-4 
61.3 
37-9 

223.2 

9-55 

189 

90.8 



149 



165.3 
20.4 

156-3 

16.4 

283 



181 
38 

IS3-S 

70.0 
50.2 
65.1 
, 66.0 
42.1 

222.3 

ii-S 

205 

90. s 



Com- 
pound. 



137 



165-3 

21.8 

257 

121. 8 

13-5 

271 



178 
33 

152-8 

64.6 
50.2 
61.2 
48.0 
39-4 

169.8 

9-7 

195 

89-8 



148 



163.7 

20.7 

247 

140.5 

13-4 

266 



183 
35 

155.4 

66.0 
50.2 
63-3 
55.6 
39.5 

196. 1 

9.6 

191 

92 



Before comparing the results of these tests to determine the 
gain from working binary, it is interesting to see that the increased 
range of temperature in this case appears to give a possible 
advantage of 9 per cent. Thus, if the engine working as a 
steam-engine only had a vacuum of 27 inches so that the lower 
temperature was about 115° F., the efficiency of Carnot's cycle 
would be 



r - r 



575 - 115 
575 + 460 



c^o, 



in which 575 is the temperature of the superheated steam supplied 
to the engine. On the other hand, with a back-pressure of 



BINARY ENGINE 283 

about 35 pounds in the sulphur-dioxide cylinder and a tempera- 
ture of about 65° F., the efficiency would be 

T - T' 575 - 65 ' 

T . 575 + 460 ^^ 

- 0.55 - 0.50 

and —"^ '^— ^ 0.00. 

. 0-55 

The results of the tests given in Table XXVIII are somewhat 
difficult to use as a basis for the discussion of the advantage of 
the binary system on account of certain discrepancies ; for example, 
tests No. 3 and No. 7 have substantially the same total power, 
steam-pressure, superheating and vacuum, and nearly the same 
vapor- pressures in the sulphur-dioxide cylinder; in fact, the 
advantage appears to lie slightly in favor of No. 7 ; nevertheless, 
the latter test is charged with 189 thermal units per horse-power 
per minute, and the former with 176, giving to it an apparent 
advantage of about 7 per cent. A comparison of steam per 
horse-power per hour gives nearly the same result. A com- 
parison of tests No. 2 and No. 4 gives even a more striking 
discrepancy, though the conditions vary more, and especially 
the total power of the latter is much greater. 

If we take 200 thermal units per horse-power per hour as the 
best result from a steam-engine, then the result from the second 
test appears to show a gain of 16 per cent, while the seventh 
test shows a gain of 6 per cent, and the fourth test is distinctly 
worse than the standard taken for the steam-engine. Under 
these conditions it is necessary to await further information. 

The last two tests made with the engine running compound 
gave results that are a trifle better than those for the compound 
engine using superheated steam but as it probably had not 
the most favorable proportions the comparison is hardly fair. 

Test No. 8 with saturated steam gave a record equivalent to 
that of the best steam-engine, which is distinctly favorable so 
far as it goes, as the steam-consumption for the steam-engine is 
large even making allowance for so poor a vacuum. 



284 ECONOMY OF STEAM-ENGINES 

Finally it appears probable that the best results for the 
binary engine could be obtained from a correctly designed 
compound engine, using superheated steam; or nearly as 
good results might be expected for saturated steam at about 
175 pounds gauge pressure with steam-jackets. Attention has 
already been called to the fact that steam-jackets accomplish 
but little with highly superheated steam, and appear to be 
unnecessary and illogical. 



CHAPTER XIII. 

FRICTION OF ENGINES. 

The efficiency and economy of steam-engines are commonly 
based on the indicated horse-power, because that power is a 
definite quantity that may be readily determined. On the 
other hand, it is usually difficult and sometimes impossible to 
make a satisfactory determination of the power actually delivered 
by the engine. A common way of determining the work con- 
sumed by friction in the engine itself is to disconnect the driving- 
belt, or other gear for transmitting power from the engine, and 
to place a friction-brake on the main shaft; the power developed 
is then determined by aid of indicators, and the power delivered 
is measured by the brake, the difference being the power con- 
sumed by friction. Such a determination for a large engine 
involves much trouble and expense, and may be unsatisfactory, 
since the engine-friction may depend largely on the gear for 
transmitting power from the engine, especially when belts or 
ropes are used for that purpose. 

The friction of a pumping-engine may be determined from a 
comparison of the indicated power of the steam-cylinders with 
the indicated work of the pumps, or, better, with the work done 
in lifting water from the well and delivering it to the forcing- 
main. But the friction thus determined is the friction of both 
the engine and the pump. Air-compressors and refrigerating 
machines may be treated in the same way to determine the fric- 
tion of both engine and compressor. Again, the combined 
friction of an engine and a directly connected electric generator 
may be determined by comparing the indicated power of the 
engine with the electric output of the generator, allowing for 
electricity consumed or wasted in the generator itself. 

The friction of a steam-engine mav consume from 5 to 15 per 

285 



.86 



FRICTION OF ENGINES 



cent of the indicated horse-power, depending on the type and 
condition of the engine. The power required to drive the air- 
pump (when connected to the engine) is commonly charged to 
the friction of the engine. It is usual to consider that seven per 
cent of the indicated power of the engine is expended on the 
air-pump. Independent air-pumps which can be driven at the 
best speed consume much less power; those of some United 
States naval vessels used only one or two per cent of the power 
of the main engines. But as independent air-pumps are usually 
direct-acting steam-pumps, much of the apparent advantage just 
pointed out is lost on account of the excessive steam-consump- 
tion of such pumps. 

Mechanical Efficiency. — The ratio of the power delivered by 
an engine to the power generated in the cylinder is the mechanical 
efficiency; or it may be taken as the ratio of the brake to the 
indicated power. The mechanical efficiency of engines varies 
from 0.85 to 0.95, corresponding to the per cent of friction given 
above. 

The following table gives the mechanical efficiencies of a 
number of engines, determined by brake-tests, or, in case of the 

Table XXIX. 

MECHANICAL EFFICIENCIES OF ENGINES. 



Kind of Engine. 



Simple engines: 

Horizontal portable 

Horizontal portable Hoadley .... 

High-speed, straight-line 

Corliss condensing 

Corliss non-condensing 

Compound: 

Portable 

Semi -portable ... 

Horizontal 

Horizontal mill-engine 

Schmidt, superheated steam .... 

Leavitt pumping-engine 

Triple-expansion Leavitt pumping-engine 




Efficiency. 



0.86 
0.91 
0.96 
0.81 
0.86 

0.88 
0.88 
0.90 
0.86 
0.92 

0-93 
0.90 



INITIAL FRICTION AND LOAD FRICTION 287 

pumping- engines, by measuring the work done in pumping 
water. 

Initial Friction and Load Friction. — A part of the friction of 
an engine, such as the friction of the piston-rings and at the 
stuffing-boxes of piston-rods and valve-rods, may be expected 
to remain constant for all powers. The friction at the cross- 
head guides and crank-pins is due mainly to the thrust or pull 
of the steam-pressure, and will be nearly proportional to the mean 
effective pressure. Friction at other places, such as the main 
bearings, will be due in part to weight and in part to steam- 
pressure. On the whole, it appears probable that the friction 
may be divided into two parts, of which one is independent of 
the load on the engine, and the other is proportional to the load. 
The first may be called the initial friction, and the second, the 
load friction. Progressive brake-tests at increasing loads con- 
firm this conclusion. 

Table XXX gives the results of tests made by Walther-Meun- 
ier and Ludwig * to determine the friction of a horizontal-receiver 
compound engine, with cranks at right angles and with a fly- 
wheel, grooved for rope-driving, between the cranks. The 
piston-rod of each piston extended through the cylinder-cover 
and was carried by a cross-head on guides, and the air-pump was 
worked from the high-pressure piston-rod. The cylinders each 
had four plain slide-valves, two for admission and two for exhaust; 
the exhaust- valves had a fixed motion, but the admission- valves 
were moved by a cam so that the cut-off was determined by the 
governor. 

The main dimensions of the engine were : 

Stroke 40.2 inches. 

Diameter: small piston 21.2 " 

large piston 31.6 " 

piston-rods 3.2 " 

Diameter, air-pump pistons 14.2 " 

Stroke, air-pump 18.8 " 

Diameter, fly-wheel 24.1 " 

* Bulletin de la Snc. Ind. de Mulhouse, vol. Ivii, p. 140. 



288 



FRICTION OF ENGINES 



Table XXX. 

FRICTION OF COMPOUND ENGINE. 

Walther-Meunier and Ludwig, Bulletin de la Soc. Ind. de Mulhouse, 

vol. Ivii, p. 140. 







Horse-Powers— Chevaux aux Vapeur. 








Condition. 


Indicated. 


Effective. 


Absorbed 
by Engine. 


Friction. 


Efficiency. 


I 




288.5 


249.0 


39-5 


°-^37 


0.863 


2 




276.9 


238.9 


38.0 


0.138 


0.862 


3 


Compound 


265.6 


228.9 


36.7 


0.139 


0.861 


4 


condensing 


243-7 


208.8 


34-9 


0.144 


0.856 


5 


with 


222.7 


188.7 


34-0 


0-153 


0.847 


6 


air-pump. 


201.5 


168.6 


32.9 


0. 164 


0.836 


7 




180.4 


148.5 


31-9 


0.178 


0.822 


8 




158. 1 


128.4 


29-7 


0.189 


O.811 


9 




136. 1 


108.3 


27.8 


0. 205 


0-795 


10 




153 -I 


128.4 


24-7 


0. 161 


0.839 


II 


High- 


142.0 


118. 3 


23-7 


0. 167 


0.S33 


12 


130.9 


108.3 


22.6 


0.173 


0.827 


13 


pressure 

cyHnder 

only. 

Condensing 

with 


120. 1 


98 2 


21.9 


0.182 


0.818 


14 


109.0 


88.2 


20.8 


0. lOI 


0.809 


\l 


97-5 
86.3 


78.1 
68.1 


19.4 
18.3 


0.199 
0. 212 


0.801 
0.788 


17 


75-7 


58.0 


17.7 


0.234 


0.766 


18 


air-pump. 


65-5 


48.0 


17-5 


0.267 


0-733 


19 




55-2 


37-9 


17-3 


o-3^3 


0.687 


20 




145-9 


128.4 


^7-5 


0. I20 


0.880 


21 




135-7 


118.3 


17.4 


0. 129 


0.871 


22 


High- 


125.2 


108.3 


16.9 


0-135 


0.865 


23 


pressure 


114.4 


98.2 


16.2 


0. 142 


0.858 


24 


cylinder 


103.9 


88.2 


15-7 


0. 152 


0.848 


25 


onlv. 


93 -o 


78.1 


14.9 


0. 160 


0.840 


26 


Non- 


82.0 


68.1 


13 9 


0.170 


0.830 


27 


condensing, 


71.7 


58.0 


13-7 


0. 191 


0.809 


28 


no air-pump. 


61.6 


48.0 


13-6 


0.221 


0.779 


29 




51-3 


37-9 


13-4 


0.262 


0.738 



The engine during the experiments made 58 revolutions per 
minute. The air-pump had two single-acting vertical pistons. 

Each experiment lasted 10 or 20 minutes, during which the 
load on the brake was maintained constant, and indicator- 
diagrams were taken. The experiments with small load on the 



INITIAL FRICTION AND LOAD FRICTION 



289 



brake (numbers 9, 18, 19, 28, and 29) were irregular and uncer- 
tain. 

The first nine tests were made with the engine working com- 
pound. Tests 10 to 19 were made with the high-pressure cyUn- 
der only in action and with condensation, the low-pressure con- 
necting-rod being disconnected. Tests 20 to 29 were made with 
the high-pressure cylinder in action, without condensation. 

The results of these tests are plotted on Fig. 60, using the 




AR8CIS8AE, EFFECTIVE HORSEPOWER. 
ORDINATES, FRICTION HORSEPOWER. 



Fig. 60. 

effective horse- powers for abcissae and the friction horse-powers 
for ordinates. Omitting tests with small powers (for which the 
brake ran unsteadily), it appears that each series of tests can be 
represented by a straight line which crosses the axis of ordinates 
above the origin; thus affording a confirmation of the assumption 
that an engine has a constant initial friction, and a load friction 
which is proportional to the load. 

Now the initial friction which depends on the size and con- 
struction of the engine may be assumed to be proportional to the 



tQO 



FRICTION OF ENGINES 



normal net or brake horse-power, P„, which the engine is designed 
to deliver, and may be represented by 

where a is a constant to be determined from a diagram like Fig. 
60. If P is the net horse-power delivered by the engine at any 
time, then the load friction corresponding is 

bp, 

where Z> is a second constant to be determined from experiments. 
The total friction of the engine will be 

F = aP, + bP, 

so that the indicated power of the engine will be 

I.H.P. = P + aP^ + bP = aP^ + (i + b)P, 

The mechanical efficiency corresponding will be 

I.H.P. - F P 



^m. — 



I.H.P. I.H.P. 



The compound condensing engine for which tests are repre- 
sented by Fig. 60 developed 290 I.H.P. and delivered 250 horse- 
power to the brake, so that 40 horse-power were consumed in 
friction. The diagram shows also that the initial friction was 
20 horse-power, and consequently the load friction was 20 
horse-power. The values of a and b are consequently 

a = 20 -4- 250 = 0.07; 

b = (40 — 20) -^ 250 = 0.07. 

The indicated horse-power for a given load P is 

I.H.P. = o.o7P„ + 1.07P. 

Similar equations can be deduced for the engine with steam 
supplied to the small cylinder only; but as the engine is not then 
in normal condition they are not very useful. 

The maximum efficiency of this engine is 

250 -f- 290 = 0.86; 



INITIAL FRICTION AND LOAD FRICTION 



591 



but at half load (125 horse-power) the indicated horse-power is 

I.H.P. = 0.07 X 250 -f 1.07 X 125 == 151, 
and the efficiency is 

125 - 151 = 0-83- 

Table XXXI. 

FRICTION OF CORLISS ENGINE AT CREUSOT. 

By F. Delafond, Annales des Mines, 1884. 

Condensing with air-pump, tests 1-33. 
Non-condensing without air-pump, tests 34-46. 











Horse-Power — Cheval h Vapeur. 




Cut-off Frac- 
tion of 


Pressure at 
Cut-off, Kilos 


Revolutions 
per Minute. 
















Stroke 


per Sq. Cm. 




Indicated. 


Effective; 


Absorbed 
by Engine. 


I 


0.039 


0.64 


64.0 


27.8 


16.3 


II-5 


2 


0.044 


2.40 


68.5 


60.0 


37.6 


22.4 


3 


0.044 


2.90 


65.0 


67.2 


45-2 


22.0 


4 


0.065 


4.90 


64.0 


117. 


88.7 


28.3 


5 


0.065 


6.20 


61.0 


138. 5 


106.3 


32.2 


6 


0.065 


7.10 


64.0 


163.2 


129.2 


34-0 


7 


0.065 


7.60 


64.0 


185.0 


144.6 


40.4 


8 


O.IOO 


0. 16 


58.0 


21.0 


10.6 


10.4 


9 


0.106 


1.55 


60.0 


61.9 


42.3 


19.6 


10 


O.IOO 


2.82 


57-3 


82:7 


61.0 


21.7 


II 


0.090 


4.80 


58.3 


135-3 


106.7 


28.6 


12 


0.128 


4.82 


58.3 


154.5 


124.8 


29.7 


13 


0.142 


0.76 


62.0 


42.3 


28.4 


13-9 


14 


0. 137 


0.71 


60.6 


44-3 


28.7 


15.6 


IS 


0.132 


2.50 


540 


795 


59.8 


19.7 


16 


0.147 


2.60 


61.6 


100. 


78.2 


21.8 


17 


0.155 


4.65 


60.0 


177.2 


145-0 


32.2 


18 


0.167 


0.22 


61.0 


40.2 


27.9 


12.3 


19 


0.197 


2.55 


57.2 


no. 8 


83-3 


27. 5 


20 


0.273 


0.40 


62.3 


50.2 


33-8 


16.4 


21 


0.264 


1.57 


633 


89.1 


61.8 


27-3 


22 


0.240 


1.64 


62.0 


87.2 


63.1 


24.1 


23 


0.245 


3.25 


56.0 


1450 


116. 


29.0 


24 


0.260 


4.76 


58.0 


209.4 


178.0 


31-4 


25 


0.335 


0.25 


590 


47.2 


32.5 


14-7 


26 


0.339 


1.94 


58.3 


III. 7 


90.0 


21.7 


27 


0.338 


2.97 


61.0 


161. 8 


1330 


28.8 


28 




0.47 


59.3 


81.3 


67.2 


14. 1 


29 




0.47 


6i.o 


80.8 


67.9 


12.9 


30 




1.60 


61.6 


148.5 


128.4 


20. 1 


31 


J 


2.70 


61.5 


216.5 


191. 


25-5 


32 




2.70 


61.5 


215-5 


191. 


24-5 


33 


0.50 


0.70 


61.5 


15.8 


0.0 


15.8 


34 


0.120 


6.00 


60.0 


132.5 


107.5 


25.0 


35 


0.106 


7.00 


53.0 


125.0 


103.0 


22.0 


36 


0. 120 


7.50 


62.0 


172.0 


148.0 


24.0 


37 


0. 150 


4.57 


S50 


102.3 


86.5 


IS. 8 


38 


0.262 


4- 50 


590 


149.2 


132.3 


16.9 


39 


0.293 


4. 55 


.59.0 


171. 8 


153-8 


18.0 


40 


0.371 


4.40 


60.0 


195. 3 


177.2' 


18. 1 


41 


0.348 


2.75 


58.0 


85.1 


73-1 


12.0 


42 


0.348 


2.75 


58. 5 


84.8 


71. 1 


13.7 


43 


0.440 


3.48 


62.0 


151. 


134-3 


T6.7 


44 


O.III 


330 


62.0 


12.8 


0.0 


12.8 


45 


0.50 


1.20 


62.0 


12.3 


0.0 


12.3 


46 


1 


0.50 


62.0 


10. 45 


0.0 


10.45 



292 



FRICTION OF ENGINES 



Table XXXI gives the results of a large number of brake- 
tests made on a Corliss engine at Creusot by M. F. Delafond, 
both with and without a vacuum, and with varying steam- 
pressures and cut-off. The tests with a vacuum are plotted 
on Fig. 61, and those without a vacuum are given in Fig. 62. 
In both figures the abscissae are the indicated horse-powers, and 
the ordinates are the friction horse-powers. Most of the tests 
are represented by dots; those tests which were made with the 
most economical cut-off (one-sixth for the engine with conden- 



4U 

35 




















^ 


















* .^ 


y 


30 
















^ 


/"^ 












. 


+ ' 


• 


y^ 


• 




25 














y 






® 










. 


^/^ 








® 


20 








• 


•^ 


^- 
















d 














15 






+ V 






Absci 


ssae^ in 


dicatec 


. horse] 


)ower 




y 


K 


c 
c 


; 


Ordin 


ates, f r 


iction 1 


lorsepo 


wer 


10 


^ 


5 


















5 














































20 



40 



60 



100 120 
Fig. 61. 



140 



160 



180 



200 



sation and one-third without) are represente.d by crosses. A 
few tests with very long cut-off, on Fig. 61, are represented by 
circles. The straight lines on- both figures are drawn to represent 
the tests indicated by crosses. In general the points representing 
tests with short cut-off and high steam-pressure lie above the 
lines, and points representing tests with long cut-off and low 
steam-pressure lie below the lines, though there are some notable 
exceptions to this rule. The circles on Fig. 61, representing 
tests with cut-off near the end of the stroke, show much less 



INITIAL FRICTION AND LOAD FRICTION 



293 



friction than the other tests. The tests on this engine show- 
clearly that both initial and load friction are affected by the 
cut-off and the steam-pressure, and that friction tests should 
be made at the cut-off which the engine is expected to have in 
service. 



25 



20 



15 



10 



















• 














• 








+ 






___^ 


^- 


+ 
















. 




Al 
Or 


Dscissat 
iinates 


, in die 
, fricti 


ited ho 
m hors 


rsepow 
jpower 


;r 























20 



4() 



60 



100 
Fig. 62. 



120 



140 



160 



180 



200 



The initial friction was eight horse-power both with and 
without condensation. But Fig. 61 shows that the engine 
with condensation gave the best economy when it indicated 
160 horse-power; the friction was then 30 horse-power, so that 
the net horse-power was 130, which will be taken for the normal 
horse-power P„. Consequently 

a = S -^ 130 = 0.06; 
^ = (30 - 8) -^ 130 = 0.17. 
.-. I.H.P. = o.o62P„ -f- 1.17P. 

In like manner Fig. 62 shows the best economy without 
condensation, for about 200 indicated horse-power, for which 
the friction is 20 horse-power, leaving 180 for the normal power 
of the engine. Consequently 

= 8 -^ 180 = 0.045; 
b = (20 — S) -T- 180 = 0.07. 
.-. I.H.P. = o.o45P„ + 1.07P. 

This engine with condensation had 36 horse-power expended 



294 



PRICTION OF ENGINES 



in friction, when developing 200 horse-power; without conden- 
sation it had 20; consequently the air-pump can be charged with 

(36 — 20) -^ 200 = 0.08 
of the indicated power. The large percentage is probably due 
to the high vacuum maintained. 

Thurston's Experiments. — As a result of a large number of 
tests on non-condensing engines, made under his direction or 
with his advice, Professor R. H. Thurston * concluded that, 
for engines of that type, the friction is independent of the 
load, and that it can, in practice, be determined by indicat- 
ing the engine without a load. 



Table XXXII. ' 

FRICTION (3F NON-CONDENSING ENGINE. 

STRAIGHT-LINE ENGINE, 8 INCHES DIAMETER, 14 INCHES STROKE. 



No. of 
Diagram. 


Boiler- 
Pressure. 


Revolutions. 


Brake H.P. 


I.H.P. 


Frictional H.I\ 


I 


50 


232 


4.06 


7.41 


3-35 


2 


65 


229 


4.98 


7.58 


2.60 


3 


63 


230 


, 6.00 


10.00 


4.00 


4 


69 


230 


7.00 


10.27 


3-27 


5 


73 


230 


8.10 


'I 75 


3-65 


6 


77 


230 


9.00 


12.70 


3.70 


7 


75 


230 


10.00 


14.02 


4.02 


8 


80 


230 


TI.OO 


14.78 


3-78 ^ 


9 


80 


. 230 


12.00 


15-17 


3-17 


10 


•^5 


230 


13.00 


[5.96 


2.96 


II 


75 


230 


14. 00 


t6.86 


2.86 


12 


70 


• 230 


15.00 


17.80 


2.80 


13 


72 


231 


20. 10 


22.07 


r.97 


14 


75 


230 


25.00 


28.31 


S'Z^ 


i5 


60 


229 


29-55 


33-04 


3-40 


16 


58 


229 


34.86 


37.20 


2.34 


17 


70 


229 


39-85 


43-04 


3-19 


18 


85 


230 


45.00 


47-79 


2 78 


19 


90 


230 


50.00 


52.60 


2.60 


20 


«5 


230. 


55-00 


57-54 


2.54 



Table XXXII gives the details of one series of tests. The 
friction horse-power is small in all the tests, and the variations 
are small and irregular, and appear to depend on the state of 

* Trans, of the Am. Soc. of Mech. Engrs., vols, viii, ix, and x. 



DISTRIBUTION OF FRICTION 



295 



lubrication and other minor causes rather than on the change 
of load. 

Distribution of Friction. — As a consequence of his conclusion 
in the preceding section, Professor Thurston decided that the 
friction of an engine may be found by driving it from some 
external source of power, with the engine in substantially the 
same condition as when running as usual, but without steam in its 
cylinder, and by measuring the power required to drive it by 
aid of a transmission dynamometer. Extending the principle, 
the distribution of friction among the several members of the 
engine may be found by disconnecting the several members, 
one after another, and measuring the power required to run the 
remaining members. 

The summary of a number of tests of this sort, made by Pro- 
fessor R. C. Carpenter and Mr. G. B. Preston, are given in 
Table XXXIII. Preliminary tests under normal conditions 
showed that the friction of the several engines was practically 
the same at all loads and speeds. 

The most remarkable feature in this table is the friction of 
the main bearings, which in all cases is large, both relatively and 
absolutely. The coefficient of friction for the main bearings, 
calculated by the formula 

33,000 H.P. 
pen 

is given in Table XXXIV. p is the pressure on the bearings in 
pounds for the engines light, and plus the mean pressure on 
the piston for the engines loaded; c is the circumference of the 
bearings in feet; n is the number of revolutions per minute, 
and H.P. is the horse-power required to overcome the friction 
of the bearings. 

The large amount of work absorbed by the main bearings 
and the large coefficient of friction appear the more remarkable 
from the fact that the coefficient of friction for car-axle journals 
is often as low as one-tenth of one per cent, the difference being 
probably due to the difference in the methods of lubrication. 



296 



FRICTION OF ENGINES 



Table XXXIII. 

DISTRIBUTION OF FRICTION. 



Parts of Engine. 



Main Bearings 

Piston and Rod 

Crank Pin . 

Cross Head and Wrist Pin 

Valve and Rod 

Eccentric Strap 

Link and Eccentric . . 
Air-Pump 

Total 





Percentages of Total 


Friction. 




Straight-line 6 X " 
Balanced Valve. 


III 


7" X 10" Lansing 
Iron Works — Trac- 
tion Locomotive 
Valve-Gear. 


12" X18" Lansing 
Iron Works — 
Automatic Bal- 
anced Valve. 


21" X 20" Lansing 
Iron Works— Con- 
densing Balanced 
Valve. 


47.0 


35-4 


35 -o 


41. 6 


46.0 


32-9 


25.0 


21.0 


49.1 




6.8 
5-4 


5-1 

4.T 


a3.o 


21.8 


2-5 

5-3 


26.4 
4.0 


22.0 


9-3 


21.0 


... 




9.0 




12.0 


100. 


100. 


100. 


100.0 


100. 



Table XXXIV. 

COEFFICIENT OF FRICTION FOR THE MAIN BEARINGS OF 
STEAM-ENGINES. 



Engine. 



6"X 12'' Straight-line . 
1 2" X 18'' Automatic (L. I 

7''Xio"Traction(L. I.W.) 
-' r''X 20'' Condensing (L. I. W.) 



W.) 







l_ 


°'Z 


M 


(^ 






1— > (U 


2 £ 


^ 3 


^■?. 


•§§ 


§^ 


og 


^a 


5.2 


a 






Q 

3 


0.85 


1500 


3-70 


2600 




0.68 


500 


2I 


3-30 


4000 


Sh 






. 10 
■19 
■31 
,09 



4) ^Tl 

o.a 



c6 

05 
08 



ft" 
11.2 

u O 



230 
190 
200 
206 



* The i2''Xi8'''' automatic engine was new, and gave, throughout, an exces- 
.sive amount of friction as compared with the older engines of the same class and 
make. 



DISTRIBUTION OF FRICTION 



297 



The second and obvious conclusion from Table XXXIII is 
that the valve should be balanced, and that nine-tenths of the 
friction of an unbalanced slide-valve is unnecessary waste. 

The friction of the piston and piston-rod is alvv^ays considerable, 
but it varies much with the type of the engine, and with differ- 
ences in handling. It is quite possible to change the effective 
power of an engine by screwing up the piston-rod stuffing-box 
too tightly. The packing of both piston and rod should be no 
tighter than is necessary to prevent perceptible leakage, and is 
more likely to be too tight than too loose. 



CHAPTER XIV. 

INTERNAL-COMBUSTION ENGINES. 

Recent advances in the generation of power from heat have 
been found in the development of internal-combustion engines 
and of steam-turbines; the latter will be treated in Chapter XIX. 
When first introduced the only convenient fuel for internal-com- 
bustion or gas-engines was illuminating-gas, which limited their 
use to small sizes, for which convenience and small cost of attend- 
ance offset the cost of fuel. Twenty years ago an engine of fifty 
horse-power was a large though not an unusual size. At that 
time Mr. Dowson had succeeded in generating gas from anthra- 
cite coal and from coke in his producer. Ten years ago engines 
of 400 horse-power were built to use Dowson producer gas, but 
as they had four cylinders the horse-power per cylinder was only 
twice that of single-cylinder engines of a decade earlier; the 
fuel used in the producer was a cheap grade of anthracite. At 
the present time, gas-engines are in use which develop as much 
as 1500 horse-power per cylinder; these engines are of the two- 
cycle double-acting type. The application of gas-engines to 
marine propulsion may now be considered to be fairly under 
way, though as yet the vessels so propelled have been of small 
displacement; certain British firms of shipbuilders have plans 
matured for the application of such engines to the propulsion 
of large ships. 

Hot-air Engines. — Though the attempt to develop hot-air 
engines on a large scale appears to be definitely abandoned, and 
though the interest of this type of engine is mainly historical a 
brief discussion of them has some advantage, for, after all, the 
internal-combustion engine is a hot-air engine in which heat is 
applied by burning fuel in the cylinder. 

In the discussion of the second law of thermodynamics {see 

298 



STIRLING'S ENGINE 



299 



page 39) it was pointed out that to obtain the maximum effi- 
ciency all the heat must be added at the highest practicable tem- 
perature, and the heat rejected must be given up at the lowest 
temperature. The hot-air engine is the only attempt to follow 
the example of Carnot's engine by supplying heat to and with- 
drawing heat from a constant mass of working substance (air). 
An attempt to obtain the diagram of Carnot's cycle from such 
an engine would involve the difficulty that the acute angle at 
which the isothermal and adiabatic lines for air cross, gives a 
very long and attenuated diagram that could be obtained only 
by an excessively large working cylinder, with so much friction 
that the effective power delivered by the engine would be insigni- 
ficant. This is illustrated by Problem 20, page 75. To obviate 
this difficulty Stirling invented the economizer or regenerator 
which replaced the adiabatic lines by vertical lines of constant 
volume, and thus obtained a practical machine. His type of 
engine is still employed, but only for very small pumping-engines 
which are used for domestic purposes, as they are free from dan- 
ger and require little attention. 

Stirling's Engine. — This engine was invented in 1816, and 
was used with good economy for a few years, and then rejected 
because the heaters, which took the place of the boiler of a steam- 
engine, burned out rapidly; the small engines now in use have 
little trouble on this account. It is described 
and its performance given in detail by Rankine 
in his "Steam-Engine." An ideal sketch is 
given by- Fig. 63. £ is a displacer piston filled 
with non-conducting material, and working 
freely in an inner cylinder. Between this 
cylinder and an outer one from A to C is 
placed a regenerator made of plates of metal, 
wire screens, or other material, so arranged 
that it will readily take heat from or yield 
heat to air passing through it. At the lower 
end both cylinders have a hemispherical head; that of the outer 
cylinder is exposed to the fire of the furnace, and that of the 




Fig. 63. 



300 



INTERNAL-COMBUSTION ENGINES 



inner is pierced with holes through which the air streams when 
displaced by the plunger. At the upper end there is a coil of 
pipe through which cold water flows. The working cylinder H 
has free communication with the upper end of the displacer 
cylinder, and consequently it can be oiled and the piston may 
be packed in the usual manner, since only cool air enters it. 

In the actual engine the cylinder H is double-acting, and 
there are two displacer cylinders, one for each end of the working 
cylinder. 

If we neglect the action of the air in the clearance of the 
cylinder H and the communicating pipe, we have the following 
ideal cycle. Suppose the working piston to be at the beginning 
of the forward stroke, and the displacer piston at the bottom of 
its cylinder, so that we may assume that the air is all in the upper 
part of that cylinder or in the refrigerator, and at the lowest tem- 
perature 7^2, the condition of one pound of air being represented 
by the point D of Fig. 64. The displacer piston is then moved 
quickly by a cam to the upper end of the 
stroke; while the working piston moves so 
little that it may be considered to be at rest. 
The air is thus all driven from the upper end 
of the displacer cylinder through the regene- 
rator, from which it takes up heat abandoned 




Fig. 64. during the preceding return stroke, thereby 

acquiring the temperature T^, and enters the 
lower end of that cylinder. During this process the line AD oi 
constant volume is described on Fig. 64. When this process is 
complete, the working cylinder makes the forward stroke, and 
the air expands at constant temperature, this part of the cycle 
being represented by the isothermal AB oi Fig. 64. At the end 
of the forward stroke the displacer piston is quickly moved 
down, thereby driving the air through the regenerator, during 
which process heat is given up by the air, into the upper part 
of the displacer cylinder; this is accompanied by a cooling at 
constant volume, 'represented by the line BC. The working 
piston then makes the return stroke, compressing the air at con- 



STIRLING'S ENGINE 



301 



stant temperature, as represented by the isothermal Hne CD, and 
completing the cycle. 

To construct the diagram drawn by an indicator, we may 
assume that in the clearance of the cylinder iJ, the communi- 
cating pipe, and refrigerator there is a volume of air which flows 
back and forth and changes pressure, but remains at the tempera- 
ture T^. If we choose, we may also make allowance for a simi- 
lar volume which remains in the waste spaces at the lower end 
of the displacer cylinder, at a constant temperature T^. 

In Fig. 65, let ABCD represent the cycle of operations, with- 
out any allowance for clearance or waste spaces; the minimum 
volume will be that displaced by the displacer piston, while the 
maximum volume is larger by the volume displaced by the work- 
ing piston. Let the point E represent the maximum pressure, 
the same as that at ^ ; and the united volumes of the clearance 
at one end of the working cylinder, of the communicating pipe, 



p 

E 




1 ^ 


tVa-v V 









^- C C' V 



Fir,. 65. 



of the clearance at the top and bottom of the displacer cylinder, 
and the volume in the refrigerator and regenerator. Each part 
of this combined volume will have a constant temperature, so 
that the volume at different pressures will be represented by the 
hyperbola EF. To fmd the actual diagram A'B'C'D', draw 
any horizontal line, as sy, cutting the true diagram at u and X, 
and the hyperbola EF at /; make uv and xy equal to st\ then 
v and y are points of the actual diagram. The indicator will 
draw an oval similar to A'B'C'D' with the corners rounded. 

The diagram in Fig. 66 was reduced from an indicator-dia- 
gram from a hot-air engine made on the same principle 



302 



INTERNAI^COMBUSTION ENGINES 



as Stirling's hot-air engine. To avoid destruction of the lubri- 
cant in the working cylinder Stirling found it advisable to con- 
nect only the cool end of the 
displacer cylinder with the working 
cylinder, and had two displacer 
cylinders for one working cylinder. 

It has been found that a good 

Fig. 66. mineral oil can be used to lubricate 

the displacer piston, and that the 
hot end also of the displacer cylinder can be advantageously 
connected with the working cylinders, of which there are two. 
Thus each working cylinder is connected with the hot end of 
one displacer cylinder and with the cool end of the other 
displacer cylinder. 

The distortion of the diagram Fig. 66 is due in part to the 
large clearance and waste space, and partly to the fact that 
the displacer pistons are moved by a crank at about 70 degrees 
with the working crank. 

A test on the engine mentioned by Messrs. Underbill and 
Johnson * showed a consumption of 1.66 of a pound of anthracite 
coal per horse-power per hour; but the friction of the engine is 
large, so that the consumption per brake horse-power is 2.37 
pounds. This engine, like the original Stirling engine, appears 
to have given much difficulty from 
the burning of the heaters. The 
difficulty is likely to be more serious 
with large than with small engines, 
as the volume of the displacer cylin- 
ders increases more rapidly than the 
heating surface. 

The action of the regenerator may 
be best explained by redrawing the 
diagram Fig. 64 on the temperature- fig. 67. 

entropy plane as shown in Fig. 67, 
where AB and CD are constant temperature lines representing 

* 'Ihcsis, M. I. T. i88q. 



T+AT M 



d IV X a 



C 



yz b 



STIRLING'S ENGINE 



303 



isothermal expansion, and DA and BC take the place of 
the constant volume lines on Fig. 64. To show that these 
lines are properly drawn, we may consider the equation 

d(j) = c„-+ (Cp- cj — 
1 V 

which was deduced on page 67. For the lines DA and 
BC the volumes are constant, so that the equation reduces to 







or transposing, 






dt T . 



but this last expression represents the tangent of the angle between 
the axis O^ and the tangent to the curve. This angle increases 
(but with a diminishing ratio) with the temperature, and as c^ 
is constant for a gas, the angle depends only on the temperature 
r, so that the curve BC is identical in form with the curve AD, 
and is merely set off further to the right; in consequence, parts 
like W X and ZY between a pair of constant temperature lines 
are identical except in their positions with regard to the axis OT. 
Suppose now that the material -of the regenerator has the 
temperature T^ at the lower end and T^ at the upper end, and 
that the temperature varies regularly from bottom to top. Sup- 
pose further that the air when giving heat to the regenerator 
(or receiving heat from it) differs from it by only an inappreci- 
able amount. Then the diagram of Fig. 67 will represent this 
ideal action correctly, and it is easy to show that its efficiency 
is the same as that of Carnot's cycle ABC'D\ For the 
amount of heat acquired by the regenerator during the opera- 
tion represented by BC, corresponding to the down stroke of 
the displacer piston, is measured by the area bBCc, and the 
heat yielded during the up stroke DA, is represented by 
the area dDAa; and these two areas are manifestly equal. 



304 INTERNAL-COMBUSTION ENGINES 

Moreover, the small amount of heat gained during the operation 
ZF at the temperature T is exactly counterbalanced by the 
heat yielded during the operation XW at the same temperature, 
so that there is no loss of efficiency; the small amounts of heat 
mentioned are represented by the equal areas zZ Yy and wWXx. 

It can be shown that one of the curves like DA may be drawn 
at random, provided that the other curve like BC is made iden-' 
tical and set off further to the right; but the matter is not of 
importance enough to warrant its discussion. 

In practice a regenerator must be at an appreciably lower 
temperature than the air from which it receives heat, and at a 
higher temperature than that to which it yields heat, as the flow 
of air is rapid. The loss of heat stored and restored per cycle 
of the original Stirling engine was estimated at five per cent to 
ten per cent. It may be proper before passing from the subject 
state that regenerators are not applicable to gas-engines in use 
at the present day. 

Gas-Engines. — The chief difficulty with hot-air engines is 
to transmit heat to' and from the working substance. In gas- 
engines this difficulty is removed by mixing the fuel with the 
air (so that heat is developed in the working substance itself), 
and by rejecting the hot gases after they have done their work. 
The fuel may be illuminating-gas, fuel-gas, or vapor of a volatile 
liquid like gasoline. It will be shown that the specific volume 
and the specific heat of the mixture of air and gas, both before 
and after the heat is developed by combustion, are not very 
different from the same properties of air. The general theory 
of gas-engines may therefore be developed on the assumption 
that the working substance is air, which is heated and cooled in 
such a manner as to produce the ideal cycles to be discussed, 
as is done by Clerk.* 

Experience has shown that in order to work efficiently, the 
mixture of gas and air supplied to a gas-engine must be com- 
pressed to a considerable pressure before it is ignited. This may 
be done either by a separate compressor or in the cylinder of the 

* The Gas and OH Engine : Dugald Clerk. 



GAS-ENGINE WITH SEPARATE COMPRESSOR 



305 



F 




engine itself; the second type of engines, of which the Otto 
engine is an example, is the only successful type at the present 
time; the other type has some advantages which may lead to its 
development. 

Gas-Engine with Separate Compressor. — This engine has 
a compressor, a reservoir, and a working cylinder. When run 
as a gas-engine a mixture of gas and air is drawn into a pump or 
compressor, compressed to several atmospheres, and forced into 
a receiver. On the way from the receiver to the working cylinder 
the mixture is ignited and burned so that the temperature and 
volume are much increased. After expansion in the working 
cylinder the spent gases are exhausted at atmospheric pressure. 

The ideal diagram is represented by Fig. 68. ED represents 
the supply of the combustible mixture to the jp 
compressor, DA is the adiabatic compres- 
sion, and AF represents the forcing into 
the receiver. FB represents the supply 
of burning gas to the working cylinder 
BC represents the expansion, and CE the 
exhaust. In practice this type of engine ^^'^^' 

always has a release, represented by GiJ, before the expansion 
has reduced the pressure of the working substance to that of the 
atmosphere. 

This type of engine has been used as an oil-engine by supplying 
the fuel in the form of a film of oil to the air after it has been 
compressed. In such case the compressor draws in air only, 
and there is not an explosive mixture in the receiver. The 
Brayton engine when run in this way could burn crude petroleum, 
or, after it was started, could burn refined kerosene. Its chief 
defect appears to have been incomplete combustion and conse- 
quent fouling of the cylinder with carbon. 

The effective cycle may be considered to be represented by 
the diagram A BCD (Fig. 68), and may be assumed to be pro- 
duced in one cylinder by heating the air from A to B, by cooling 
it from C to D, and by the adiabatic expansion and compression 
from B io C and from D io A. If T^ and Tf, are the absolute 



o 



3o6 INTERNAI^COMBUSTION ENGINES 

temperatures corresponding to the points A and B, then the 
heat added from A to B is 

c, {T, - rj, 
and the heat withdrawn from C to P is 

Cj, {T, - Ta), 
so that the efficiency of the ideal cycle is 

c, {T, - rj T,-T,- ^'"^ 

But since the expansion and compression are adiabatic, 



but p^ = pa and Pt = p„ therefore 

I t — I 

so that the equation for efficiency becomes 



(178) 



This discussion of ideal efficiency is due to Dugald Clerk,* and 
has the advantage of replacing an exceedingly complex operation 
by a simple ideal operation which has approximately the same 
efficiency. How far the ideal cycle can be used to determine 
the probable advantages of certain conditions depends on the 
degree of approximation, — a matter which will be referred 
to later. It must be admitted that the divergence of the 
actual from the real cycle is much greater than the divergence 
of the steam-engine cycle from that of a non-conducting 
cylinder. 

For example^ with the pressure in the reservoir at 90 pounds 

* The Gas Engine, 1886; The Gas and Oil Engine, 1896. 



GAS-ENGINE WITH SEPARATE COMPRESSOR 



307 



above the atmosphere the efficiency is 



1 .405 — I 

.405 



(^^^ = -43. 

\14.7 + 90/ 



When the cycle is incomplete the expression for the efficiency 
is not so simple, for it is necessary to assume cooling at constant 
volume from G to H (Fig. 68), and cooling at constant pressure 
from H to D; so that the heat rejected is 

c. {T, - Tn) + c, (T, - r,), 
and the efficiency becomes 

- (T, - T,) + {T, - T,) 
e-^-- ^_-^r . . . .(179) 

For example^ let it be assumed that the pressure at A is 90, 
pounds above the atmosphere, that the temperature at B is 2500° 
F., and that the volume at G is three times the volume at B. 

First, the temperature at A is 



provided that the temperature of the atmosphere is 60° F. 
The temperature at G is 

^'=^'G;r'= ^960(^-^=1897, 

and the pressure at G is 

(I'.V /iy-405 

- ) = (14.7 +9o)(-) - 22.4 pounds, 
^(/ ^3 ' 

so that the temperature at H is 

r.= r,^= .897X^:1.,,,,, 

and finally the efficiency is 



(1897 - 1247) + 1247 - 520 



« = I ^^-^ 7 = 0.42.. 

2960 — 917 



3o8 INTERNAI^COMBUSTION ENGINES 

Gas-Engines with Compression in the Cylinder. — All success- 
ful gas-engines of the present day compress the explosive mixture 
in the working cylinder. Very commonly they take gas at one 
end of the cylinder only, and require four strokes to complete 
the cycle, so that there is one explosion for twa revolutions when 
working at full power. Such engines are commonly known as 
four-cycle engines. Some engines have the exhaust and filling 
of the cylinder accomplished in some other way, and are known 
as two-cycle engines; they have an explosion for every revolu- 
tion when single-acting. Both four-cycle and two-cycle engines 
have been made double-acting in large sizes. The first forward 
stroke of the piston from the head of the cylinder draws in the 
mixture of gas and air, which is compressed on the return stroke; 
at the completion of this return stroke the mixture is ignited and 
the pressure rises very rapidly; the next forward stroke is the 
working stroke, which is succeeded by an exhaust-stroke to 
expel the spent gases. In almost all engines these four strokes 
are of equal length, for the advantage of making them of unequal 
length, as required for the best ideal cycle, is more than coun- 
terbalanced by the mechanical difficulty of producing unequal 
strokes. 

The most perfect ideal cycle, represented by Fig. 69, has 

four strokes of unequal length so 
arranged that the piston starts from 
the head of the cylinder when gas 
is drawn in, and the pressure in the 
cylinder is reduced to that of the 
atmosphere before the exhaust stroke. 
Thus there is the filling stroke, 
represented by EC\ the compression 
stroke, represented by CD\ the 
working stroke, represented hy AB; 
' Fig. 69. and the exhaust stroke, represented 

by BE. 
The effective cycle is ABCD, which may be considered to 
be performed by adding heat at constant volume from D to A, 




GAS-ENGINES WITH COMPRESSION IN THE CYLINDER 309 

and withdrawing heat at constant pressure from B to C, together 
with the adiabatic expansion and compression AB and CD. 
The heat added under this assumption is 

cATa - T,), 

and the heat rejected is 

so that the efficiency is 

c. {T, - Ta) T,-T, ^ ^ 

If the temperature at A and the pressure at D are assumed, 
then it is necessary to make preliminary calculations of the 
temperatures at D and at B before using equation (180). Thus, 
adiabatic compression from C to D gives for the temperature 
at D 

K — X 

T,= T,{^ ...... (181) 

in like manner adiabatic expansion from A io B gives 



r» = r„ (|?l) (,82) 

in which the value of pa may be calculated by the equation 

p. = p, ~ (183) 

since the pressure rises with the temperature at constant volume 
from D \.o A. 

For example, if the pressure at the end of compression is 
90 pounds above the atmosphere, and the temperature at the 
end of the explosion is 2500° F., then 

0405 

r,= (6o+46o)(li:I±^y"=9i7, 

\ 14.7 ' 



3IO 



INTERNAL-COMBUSTION ENGINES 



provided that the temperature of the atmosphere is 60° F. 

2500 + 460 
917 



pa = 104.7 — ^ \J^ = 338 pounds; 

•405 

(\ "-405 
^lll-j = 1199; 




Fig. 70. 



represented by GC. 



338 

IIQQ — S20 

2960 — 917 

If the expansion is not carried to the 
atmospheric pressure, then the diagram 
shows a release at the end of the stroke, 
as in Fig. 70, and the cycle must be 
considered to be formed by adding 
heat as before at constant volume, but 
by withdrav^ing heat at constant volume 
to cause a loss of pressure from B to 
G, and by ^withdrawing heat at con- 
stant pressure, during the process 
The heat rejected becomes, therefore, 



and the efficiency is 

_ cATg - Tg) -CAT, - TJ 



' pC^^ 



Tc) 



= I 



c^ (Ta - Ta) 
T, + K (T, - T,) 



Ta 



(184) 



Assuming, as before, the pressure at D and the temperature 
at ^, it becomes necessary to find the temperatures at B and at 
G as well as the temperature at D\ this last may of course be 
found by equation (181). If the pressure at B is assumed also, 
then equations (182) and (183) may be used as before to find 
7^5 ; and Ty may be found by the equation 



T,= r> 



(185) 



GAS-ENGINES WITH COMPRESSION IN THE CYLINDER 311 

For example J let it be assumed that the expansion ceases 
when the pressure becomes 20 pounds above the atmosphere, 
the other conditions being as in the previous example. Then 



40s 



(2 



500 + 460) f — i— — \ = 1536; 



and 



r,= 1536^ = 650; 

34-7 



e= J - 1536 - 650 + 1.405 (650 - 520) _ ^^^g^ 
2960 — 917 

Though not essential to the solution of the example, it is 
interesting to know that the volume at C is 



\ 14.7 / 



4 + 



times the volume at D, and that the volume at 5 is 



<34-7/ 



5 + 



times the volume at A. 

When, as in common practice, the 
four strokes of the piston are of equal 
length, the diagram takes the form shown 
by Fig. 71; the effective cycle may be 
considered to be equivalent to heating at 
constant volume from D io A and cooling 
at constant volume from B to C, together 
with adiabatic expansion and compression 
from ^ to ^ and from C to Z) 





A 










D 


\^^^B 





E 




"~-^C 




V 



Fig. 71. 



312 INTERNAL-COMBUSTION ENGINES 

The heat applied is 
and the heat rejected is 
so that the efficiency is 

Since the expansion and compression are adiabatic, we have 
the equations 

T.v,'^-' = TgV,^-\ and T,v,^-' = T^ v^"-') 

but the volumes at A and D are equal, as are also the volumes 
at B and C; consequently by division 

consequently 

T, - n T, T, 






and the expression for efficiency becomes 

ft)- <■»') 



e = I 



which shows that the efficiency depends only on the compression 
before explosion. 

For example^ if the volume of the clearance or compression 
space is one-third of the piston displacement, so that v^ is one- 
fourth of Vc, then the efficiency is 

0.405 



e=^ 1 - \-j = 0.43. 



The pressure at the end of compression is 



GAS-ENGINES WITH COMPRESSION IN THE CYLINDER 313 

pounds absolute, or 88.4 pounds by the gauge. The calculated 
efficiency is therefore not much less than the efficiencies found for 
other examples; it is notable that the efficiency is nearly the 
same as that calculated on page 307 for an engine with separate 
compression to 90 pounds by the gauge. For the case in hand, 
however, the pressure after explosion, which depends on the 
temperature, may exceed 300 pounds per square inch. 

The diagrams from engines of this type * resemble Fig. 72, 




Fig. 72. 



which was taken from an Otto engine in the laboratory of the 
Massachusetts Institute of Technology. During the filling 
stroke, the pressure in the cylinder is less than that of the atmos- 
phere; the charge is ignited just before the end of the compression 
stroke, and the explosion though rapid is not instantaneous, 
as is indicated by the rounding of the corners of the diagram 
at both the bottom and the top of the explosion line, and by 
the leaning of that line to the right. Release occurs before the 
end of the stroke, and there is considerable back pressure during 
the exhaust stroke. The scale of the diagram is 150 pounds to 
the inch, and the maximum pressure is 251 pounds. The atmos- 
pheric line is omitted to avoid confusion. 

In order to show clearly the conditions during the exhaust 
and filling strokes, the diagram Fig. 73 was taken with a scale 

* A description of a four-cycle gas-engine will be found on page 337, and may 
be read for the first time in this connection. 



314 INTERNAL-COMBUSTION ENGINES 

of 20 to the inch, and with a stop to limit the rise of the indicator- 
piston; the upper part of the diagram consequently does not 
appear in the figure. The mean back-pressure is about five 
pounds, and the reduction of pressure in the cylinder is between 




Fig. 73. 

three and four pounds below the atmosphere. Reference to 
the influence of the negative area of Fig. 73 on the effective 
indicated horse-power will be made later. 

The compression line does not differ very much in appearance 
or in reality from an adiabatic line from air, though the air may 
be expected to receive heat from the walls of the cylinder during 
the first part of the compression stroke, and may part with heat 
during the latter part. The expansion line has a resemblance 
to the adiabatic line for air, but is usually less steep, especially 
for large engines; but in reality the conditions in the cylinder 
are very different, for the combustion does not cease at the max- 
imum pressure, but continues more or less during the expansion 
stroke, and may extend to the release; and at the same time 
heat is taken up energetically by the walls of the cylinder, which 
are cooled by a water-jacket to avoid overheating. These two 
effects, after-burning and loss of heat to the water-jacket, deter- 
mine the form of the expansion line and its resemblance to an 
adiabatic line. 

Characteristics of Gases. — There are three distinct kinds of 
gases used in gas-engines: (i) illuminating-gas, (2) producer- 
gas, (3) blast-furnace gas. Each class has fairly well-marked 
characteristics, though there is considerable variation in a class. 
The greatest variation is liable to be found in blast-furnace 
gas, since the metallurgical operations are of the first importance, 



CHARACTERISTICS OF GASES 



315 



and, if the gas is to be used for generating power, the engines 
and adjuncts must be adapted to the conditions. Producer- 
gas is made from coke, anthracite, or from non-caking bituminous 
coal, and consists mainly of hydrogen and carbon monoxide, diluted 
with the nitrogen of the air, together with five or ten per cent 
of carbon dioxide and a small percentage of hydrocarbons espe- 
cially when bituminous coal is used. Illuminating-gas is now 
commonly made by the water-gas process, which yields a gas not 
very unlike producer-gas, but that gas is enriched with hydro- 
carbons of varying composition; formerly illuminating-gas was 
distilled from gas-coal, which was a rich bituminous coal yielding 
a large percentage of hydrocarbons when distilled. 

The general characteristics of illuminating-gas are represented 
by the following analysis of Manchester coal-gas quoted from 
the first edition of Clerk's Gas Engine, and used by him to 
investigate the effect of combustion on the volume of the gas. 

ANALYSIS OF MANCHESTER COAL-GAS. (Bunsen and Roscoe.) 



CO 



Hydrogen, H . . 
Methane, CH^ . 
Carbon monoxide 

Ethylene, C2H4 

Tetrylene, C4Hg 

Sulphuretted hydrogen, H^S 

Nitrogen, N 

Carbon dioxide, CO, . . . 



Vols 



Total I 100.00 



Vols. O lequired 

for 

Combustion. 



22 


79 


69 


8 


3 


32 


12 


24 


14 


28 





43 







Products. 
Vols. 



45 

104 

6 

16 

19 
o 
2 
3 



58, H,0 

7> 

64, CO2 

32, CO2 & H2O 

04, CO2 & H2O2 

58, H2O & SO2 

46 

67 



122.86 O 198.99, C02,H2 0& SO2 



An analysis of illuminating-gas made by the water-gas process 
at Boston gave: Hydrogen 27.9, methane 28.9, carbon monoxide 
25,3, carbon dioxide 1.9, hydrocarbons 12.0, nitrogen 3.0, oxygen 
i.o; the analysis being only proximate does not allow of a calcu- 
lation of the oxygen required for combustion. 

The following composition of producer-gas was taken from a 
report of tests on a gas-engine by Professor Meyer, for which 



3i6 



INTERNAL-COMBUSTION ENGINES 
COMPOSITION OF PRODUCER-GAS. 





Vols. 


Vols, of 
Oxygen for 
Combustion. 


Products 
Vols. 


Hydrogen, H . . 


13-7 
0.7 

24.6 

6.5 

•5 

54-0 


6.8 
1.4 
12.3 





13.7 H2O 
2.1, CO2 &H2O 
24.6, CO2 
6.5. CO2 
0.5,0 

54-0, N 


Methane, CH4 ......... 

Carbon monoxide, CO .... 

Carbon dioxide, COg 

Oxygen, O 


Nitrogen, N 






100 


20.5 


101.4 



details are given on page 350. Eight analyses are given in the 
original paper, v^hich are here averaged. 

Rich non-caking bituminous coals may shov^ a considerably 
larger proportion of hydrogen. 

In a paper on the use of blast-furnace gas Mr. Bryan Donkin 
gives the composition of gases from five furnaces in England, 
Scotland, and Germany, from which the average values in the 
folio v^ing table vv^ere deduced: 

COMPOSITION OF BLAST-FURNACE GAS. 





Vols. 


Vols, of 

Oxygen for 

Combustion. 


Products. 
Vols. 


Hydrogen, H 

Carbon monoxide, CO . . . . 

Carbon dioxide, CO2 

Nitrogen, N. 


2-5 

29.1 

7.0 

61.4 


1-3 
19.6 





2.5, H2O 

29.1, CO2 

7.0, CO2 

6i.4,N 






100 


20.9 


TOO 



Not only is there much variation in the composition of gases 
from different blast-furnaces, but the variation v^ith the progress 
of the metallurgical operations is so marked that it is customary 
to mingle the gases from several furnaces in order to insure 
that the gas is proper for use in gas-engines. 



CHARACTERISTICS OF GASES 



317 



The amounts of oxygen required for the combustion of a given 
volume of any gas can be computed from the formulae rep- 
resenting the chemical changes accompanying combustion, 
together with the fact that a compound gas occupies tv^o volumes, 
if measured on the same volumetric scale as the component 
gases. Thus two volumes of hydrogen with one volume of 
oxygen unite to form superheated steam as represented by the 
formula 

2H + O = Ufi, 

and the three volumes after combustion and reduction to the 
original temperature are reduced to two volumes; in this case, 
to have the statement hold, the original temperature would need 
to be very high, to avoid condensation of the steam into water. 
But in the application to gas-engines this leads to no inconven- 
ience, because the gases after combustion remain at a high tem- 
perature till they are exhausted, and the laws of gases can be 
assumed to hold approximately. A compound gas like methane 
can be computed as follows: 

CH, +40== CO2 + 2H2O. 
Since the compound gas methane occupies two volumes and 
requires four volumes of oxygen, it is clear that each cubic foot 
of that gas will demand two cubic feet of oxygen; the total volume 
may be reckoned as six before combustion, and in like manner 
there will be six volumes after combustion, namely, two of 
cairbon d^ioxide and four of steam. 

In this way the oxygen required for combustion of the three 
kinds of gas for which the compositions arc given, has been 
computed, and also the volumes after combustion. For coal- 
gas the contraction due to the combustion of hydrogen and 
carbon monoxide is very nearly compensated by the expansion 
due to the breaking up and combustion of the hydrocarbons. 
A similar result may be expected for any illuminating-gas. On 
the other hand, producer-gas if burned in oxygen would show a 
contraction of 

I20.t: — IOI.4 IQ 

= -^- = 0.16; 

120.5 ^20 



3i8 INTERNAI^COMBUSTION ENGINES 

but in practice the producer-gas is mixed with 1.3 to 1.5 of its 
volume of air, so that the contraction of 19 volumes takes place 
in 230 to 250 volumes, and thus is therefore of yV to 8 per cent 
contraction. 

Clearly this matter has to do with the question raised on 
page 306, as to the reliance to be placed on the ideal efficiencies 
which assume heating of air instead of combustion of fuel. 
For illuminating-gas that assumption appears unobjectionable, 
and for producer- gas the discrepancy is not so great as to 
destroy the value of the method. 

Temperature after Explosion. — The most difficult question 
concerning the theoretical thermal efficiency of gas-engines is 
the determination of the temperature after explosion. Direct 
determination is difficult both on account of the high tempera- 
ture and the very short interval of time during which the maxi- 
mum temperature can be considered to exist. 

A comparatively simple calculation of the temperature after 
explosion can be made from a diagram like Fig. 72, if the com- 
pression can be assumed to be adiabatic, and if the laws of 
perfect gases can be applied. The pressure on the compression 
line measured on an ordinate through the point a of maximum 
pressure, is 61 pounds, or 75.7 pounds absolute. If the tem- 
perature of the gases in the cylinder at atmospheric pressure is 
taken to be 70 degrees, adiabatic compression gives approxi- 
mately 



o) (1-^' 
\i4.7/ 



r,= (70 +460) U^) =847°. 

The maximum pressure after explosion is 251 pounds, or about 
266 pounds absolute. If the temperature at constant volume 
is assumed to be proportional to the absolute pressure, we have 

^47 X-— =2975, 

/5-7 

or about 2500° F. This result, which depends on the assumption 
that the properties of the charge in the cylinder of a gas-engine 



AFTER BURNING 



319 



are and remain the same as those of gases at ordinary tempera-, 
tures, can be taken as a first approximation only. 

In connection with tests on a gas-engine (see page 350) using 
illuminating-gas, Professor Meyer makes a careful investigation 
of the temperature which might be developed in the cylinder 
of a gas-engine if the charge were completely burned in a non- 
conducting cylinder. The results only will be quoted here. 
The composition of the gas will be found on page 316, from 
which it appears that it was probably coal-gas resembling 
Manchester gas, and not differing very radically from Boston 
gas, by use of which Fig. 72 was obtained. The pressure at 
the end of compression was 69 pounds by the gauge, and after 
explosion was 220 pounds, so that the conditions were not very 
different from those of Fig. 72, except that the pressure on the 
compression line is not on the ordinate for measuring the max- 
imum pressure, and therefore the parallel calculation cannot be 
made. 

On the assumption of constant specific heats Professor Meyer 
finds that complete combustion should give 4250° F. in a non- 
conducting cylinder, but using Mallard and Le Chatelier's 
equation for specific heats at high temperatures he gets 3330*^ F. 
Those experimenters report that dissociation of carbon monoxide 
begins at about 3200° F., and of steam at about 4500° F.; but 
the dissociation is slight at those temperatures. Though the 
subject is still obscure, it appears fair to assume that the failure 
to reach the temperatures which can be computed for complete 
combustion, can be charged in part to suppression of combustion 
on account of the high temperature in the cylinder. 

After Burning. — Accompanying the suppression of heat on 
account of the approach to the temperature of dissociation is 
the development of heat during expansion which extends in some 
cases to release, as is indicated by a flicker of flame into the 
exhaust; explosions in the mufflers of automobiles are attributable 
to this action. The fact that the expansion curve approaches 
the adiabatic line during expansion is indirect evidence of after- 
burning, because the water-jacket withdraws heat at the same 



320 INTERNAL-COMBUSTION ENGINES 

time. The actual expansion line is less steep than the adiabatic 
for gas, and for large gas-engines can approach the condition 
represented by the equation 

pv ^'^ = const.; 

but a part of this action can be attributed to the presence of 
carbon monoxide and steam in the products of combustion, which 
may reduce the exponent of the adiabatic Hne from 1.405 to 1.37. 

Water-jackets. — All except very small internal-combustion 
engines have the heads and barrels of the cylinder cooled by 
w^ater-jackets ; large engines commonly have the pistons cooled 
with water, and double-acting engines have the piston-rods and 
stuffing-boxes cooled. Not uncommonly the valves of large 
engines are cooled, and if such engines use rich gases, extra 
cooling surface is provided in the charging space or cartridge 
chamber; the latter device is to avoid pre-ignition, and the 
former is in part for the same purpose. 

Primarily, water-jackets are to protect the metal of the cylinder 
and to make lubrication possible. The use of jackets and other 
cooling devices has been considered a mechanical necessity, which 
many inventors have sought to avoid; but it appears likely that 
it is only a question whether the heat shall be withdrawn by a 
water-jacket, or whether the heat shall be suppressed by dissocia- 
tion and thrown out in the exhaust. Large engines, which have 
less exposed area per cubic foot of cylinder contents, show a less 
percentage of heat withdrawn by the jacket, but a larger per- 
centage thrown on in the exhaust; the balance is, however, in 
favor of large engines which show a better economy. 

Economy and Efficiency. — It is customary and altogether 
desirable to rate the economy of gas-engines and other internal- 
combustion engines in thermal units per horse-power per minute; 
this was found to be desirable, if not necessary, for studying 
the means of improving the performance of steam-engines. But 
as steam-engines are commonly rated in terms of steam per 
horse-power per hour, so also gas-engines have been rated in 
terms of cubic feet of gas per horse-power per hour, and gasoline- 



ECONOMY AND EFFICIENCY 



321 



and oil-engines have been rated in pounds of fuel per horse- 
power per hour. The variation in the fuel used for such engines 
makes the secondary methods less satisfactory than rating engines 
on steam-consumption, so that it should be employed only when 
the calorific capacity of the fuel cannot be determined or 
estimated. 

Since the heat-equivalent of a horse-power is 42.42 thermal 
units per minute, the actual thermal efficiency of an internal- 
combustion engine can be determined by dividing that figure 
by the thermal units consumed by the engine per horse-power 
per minute. For example, the engine tested by Professor Meyer 
used about 170 thermal units per horse-power per minute, 
and its thermal efficiency was 0.25, using the indicated horse- 
power. The ratio of the cartridge space to the whole volume 



was 



— —, so that equation (187) gives in this case 0.42 for the 



nominal theoretical efficiency; consequently the ratio of the 
efficiencies is nearly 0.60. 

By a somewhat intricate method Professor Meyer computed 
the efficiency for two tests on the engine for which details are 
given on page 350, on the assumption that complete combustion 
occurred in a non-conducting cylinder. The ratio of gas to air 
in one test was one to 8.9, and in the other one to 12. Assuming 
that the specific heat of the mixture in the cylinder before and 
after explosion, remained constant, he found for the first test 
an efficiency of 0.398, and for the second 0.403; but making use 
of Mallard and Lc Chatelier's investigations on specific heats at 
high temperatures, he found for the efficiencies 0.297 and 0.318. 
The values for constant specific heat differ but little from the 
nominal theoretical efficiency; in fact, if the exponent be reduced 
from 0.405 to 0.38, the nominal efficiency becomes 0.40, which 
is a very close coincidence. But the efficiencies computed from 
the heat-consumptions for these two tests are 0.253 ^-nd 0.249. 
If then the nominal theoretical efficiency, or the efficiency which 
Professor Meyer calculated on assumption of constant specific 



322 INTERNAL-COMBUSTION ENGINES 

heat, be taken as the basis of comparison, the engine gave for 
the ratio of actual to theoretical efficiency, 

0.253 -^ 0.398 = 0.64, or 0.249 ^ 0.403 =^ 0.62. 
If, however, we take his second values with variable specific heat, 
we have 

0.253 -J- 0.297 ^ o-^Sj or 0.249 H- 0.318 = 0.78. 

Professor Meyer uses these computations to emphasize the 
importance of better knowledge of the properties of the working 
substance in the cylinder of an internal-combustion engine; 
because, if the nominal theoretical efficiency be taken for the 
basis of comparison, there appears to be room for material 
improvement in the economy of the engine; whereas, if the 
second set of computations is taken as the basis, there is little 
prospect of improvement. In conclusion, attention is called to 
the fact that these tests were on a small engine which developed 
only ten brake horse-power. 

In the discussion of efficiency we have thus far made use of the 
heat-consumption per indicated horse-power, which is proper, 
because the fluid efficiency (or the efficiency of the action of the 
working substance) should for this purpose be preserved from 
confusion with the friction and mechanical efficiency of the 
engine. For the same reason, and also because the power of a 
steam-engine can be determined satisfactorily by the indicator, 
we used indicated horse-power in the discussion of steam-engine 
economy. There is, however, a reason why the indicated power 
is not a satisfactory basis for the discussion of the economy of 
internal -combustion engines, namely, the fact that a series of 
successive diagrams taken without removing the pencil from the 
paper on the indicator drum, will show a wide dispersion, due 
to the varying explosive action in the cylinder even when con- 
ditions are most favorable. When the engine is governed by 
omitting explosions, this difficulty is much aggravated on account 
of the negative work of idly drawing in, compressing, and expel- 
ling .air. 

Fig. 74 shows a diagram taken from the same engine as Fig. 
72, page 313, but with a fifty-pound spring and a stop to prevent 



ECONOMY AND EFFICIENCY 



323 



the indicator piston from rising too high which exhibits the 
effects of an idle cycle and other features. A portion of the 
expansion curve is shown, with oscillations due to the piston 
suddenly leaving the stop. The exhaust of the spent gases is 




Fig. 74. 

shown by the curve ah, after which the engine draws a charge 
of air (without gas) and compresses it on the upper curve from 
c to d\ on the return stroke the indicator follows the lower 
curve from d to c, so that the loop represents work done by the 
engine; finally the air is exhausted, while the indicator draws 
the line ce. To explain the difference between the exhaust lines 
ah and ae with spent gas and with air only, it may be noted that 
there is a marked drooping of the exhaust line a to about one- 
fifth of the stroke from h] this feature is more marked in Fig. 73, 
which shows the exhaust stroke to a larger scale. This droop 
may be attributed to the inertia of the column of gas in the 
exhaust pipe; the smaller volume of air which is exhausted with 
gradually rising pressure does not happen to develop this feature 
in such a way as to produce the result shown in Fig. 73. This 
drop of pressure in the exhaust pipe may be accentuated by 
adjusting the length of the exhaust pipe so as to give a partial 
vacuum just before the engine takes its next charge; when this 
action is obtained, the air-valve is opened before the gas-valve, 
and fresh air is drawn through the cyhnder to produce a scav- 
enging effect before the engine takes a new charge. At one 



324 INTERNAL-COMBUSTION ENGINES 

time considerable importance was given to scavenging to clear 
out spent gas, but it attracts less importance now for four-cycle 
engines. 

In indicating a gas-engine, allowance is, of course, made for 
the negative work of exhaust and filling; if an explosion is missed, 
allowance for the negative work for the operation shown on 
Fig. 74 should be made for each idle cycle, and when the engine 
has only a few working cycles the error of taking proper account 
of the negative work may be very large. This is, of course, 
another reason why comparisons are best based on brake horse- 
power. As can be seen from Table XXXV on page 350, the 
mechanical efficiency may range from 60 per cent to 80 per cent, 
depending mainly on the power developed; these figures are for 
continuous explosions, and the efficiency is liable to be much 
reduced if explosions are omitted at reduced power. 

Two-cycle engines commonly have a compression pump 
which supplies the mixture of gas and air at a pressure of five or 
ten pounds above the atmosphere; in such case the work of com- 
pression must be determined separately and allowed for, in the 
measurement of the indicated horse-power. 

Valve-Gear. — The supply and exhaust parts for an internal- 
combustion engine are always separate, so that there are at 
least two valves (or the equivalent) for each working end of a 
cylinder; there is also for a gas-engine a separate valve for 
admitting or controlling the supply of gas. The valves are 
usually plain disk or mushroom valves with mitered seats; in 
some cases double-beat valves are used on large engines. Very 
commonly two-cycle engines exhaust through ports cut through 
the cylinder walls and opened by the piston itself, which over- 
runs them near the end of its stroke; in at least one case the 
exhaust-valves of a four-cycle engine are water-cooled hollow 
piston-valves, but that construction appears to be exceptional. 

The exhaust-valves are always positively controlled, since they 
must remain closed against pressure in the cyHnder until the 
proper time. The inlet valves may be operated by the pressure 
of the operating fluid, opening during the suction stroke and 



STARTING DEVICES 



325 



remaining closed during the compression, expansion, and exhaust 
strokes; but very commonly the admission valves both for air 
and for gas (when the latter are separate) are positively con- 
trolled, and for very high speeds this action is necessary. 

From what has been said, it will be evident that the general 
problem of the design of the valve-gear for an internal-combus- 
tion engine resembles that for a four-valve steam-engine, espe- 
cially that type of steam-engine valve-gear which uses simple 
lift-valves. The solution which is most evident and most com- 
monly chosen is some form of cam-gear; usually the valves are 
held shut by springs, and are opened by cams on a cam-shaft 
either directly or through linkages. This cam-shaft is conven- 
iently placed parallel to the axis of the cylinder and driven* from 
the main shaft through bevel-gears; the four-cycle engine has 
the gear in the ratio of one to two, so that the cam-shaft makes 
one revolution for two revolutions of the engine in order to 
properly time the four principal operations of the cycle. The 
spring closing a valve must be properly designed not only to 
give the required pressure to hold the valve shut, but to provide 
the proper acceleration so that the valves shall remain under 
the control of the cam when closing. The cam-shaft, in addi- 
tion to the cams for the normal action of the engine, carries cams 
which facilitate starting the engine. 

Starting Devices. — Since an internal-combustion engine must 
do the work of drawing in and compressing its charge before 
energy is developed by explosion, some special device is required 
to start such an engine, involving the use of power from an 
external source. It is seldom if ever convenient .to apply power 
sufficient to start an engine under its load, and consequently 
there must be some disengagement gear to allow the engine to 
start without load, except in cases where the load is developed 
only as the engine comes up to speed. 

A small engine can be started by hand, by turning the fly- 
wheel or by working a special hand-gear; the latter should have 
a ratchet or clutch which will release or throw it out of gear 
as soon as the engine starts. The engine is driven by hand until 



326 INTERNAL-COMBUSTION ENGINES 

the operations of charging, compressing, and igniting are per- 
formed, whereupon the engine should start promptly. Except 
for very small sizes, there is a special cam that may be thrown 
into action, and which holds the exhaust-valve open till the 
piston has completed about half the compression stroke, during 
which the charge is partially wasted ; by this device the labor of 
compression is much reduced. When an engine is started in 
this manner the ignition should be delayed until the piston is 
past the dead-point, otherwise the engine is liable to start back- 
ward. The disengagement clutch will not act in such case, 
and there is great danger of an accident. 

When electric or other external power can be substituted for 
hand-power, this method can be used for starting engines of 
large size. 

A very common device is to start the engine with compressed 
air from a tank at a pressure of loo to 200 pounds per square 
inch. This air is supplied to the tank by a pump driven by 
the engine when necessary. To start the engine the cylinder is 
disconnected temporarily from the ordinary gas and air supply, 
and is worked Hke a compressed-air engine until well under 
way, whereupon the compressed air is shut off and the normal 
action is restored. The air can be supplied from the tank by 
valves controlled by hand or by a special gear. If the engine 
has more than one cylinder, compressed air may be supplied to 
one only, and the other cylinder (or cyUnders) may act in the 
usual manner, except that the compression may be reduced till 
the engine is started. 

At one time gas was withdrawn from the cylinder during the 
compression stroke, and stood in a reservoir to be used for start- 
ing. Such gas could be used at a pressure of 60 to 90 pounds, 
to start the engine as just described; or the piston could be set 
beyond the dead-point ready to start, gas could be supplied 
under pressure and ignited. There is, of course, some objection 
to the storage of explosive mixtures, though there is no reason 
why the reservoir should not be made able to endure an explosion. 

Governing and Regulating. — There are four ways available 



GOVERNING AND REGULATING 



327 



for controlling the power of an internal-combustion engine: (i) 
by regulating the proportion of air and fuel, (2) by regulating 
the amount of air and fuel without changing the proportion, 
(3) by omitting the supply of fuel during a part of the cycles, (4) 
delaying ignition. 

(i) Regulation by controlling the supply of fuel is the normal 
method for engines working on the Joule or Brayton cycle with 
compression in a separate cyUnder, for which a theoretical dis- 
cussion is given on page 305. For this cycle there is no explo- 
sion, but the gaseous or liquid fuel can be burned during admis- 
sion in any proportion. 

The Brayton engine had a double control for variation in 
load. In the first place a ball-governor shortened the cut-off 
for the working cylinder when the speed increased on account 
of reduction in the load; this had the effect of raising the pres- 
sure in the air reservoir into which the air-pump delivered, since 
that pump delivered nearly the same weight of air per stroke 
under all conditions. In the second place, there was an arrange- 
ment for shortening the stroke of the little oil-pump when the 
pressure increased; so that indirectly the amount of fuel was 
proportioned to the load. A similar effect was produced when 
the engine was designed to use gas. 

For the Diesel motor, to be described later, the fuel supply 
can be adjusted to the power demanded for all conditions of 
service. 

But for gas-engines it has not been found practicable to con- 
trol the engine by regulating the mixture of gas and air except 
within narrow ranges. This comes from the fact that very rich 
or very poor mixtures of gas and air will not explode. Experi- 
ments at the Massachusetts Institute of Technology show that 
illuminating-gas will explode at atmospheric pressure with 
the ratio of gas to air varying from 1 115 to i : 3.5. Weaker mix- 
tures can be exploded in a gas-engine after compression. Again, 
gas may be supplied in such a way that the mixture near the 
point of ignition may be rich enough to explode promptly and 
fire the remainder of the charge. The ignition of weak mix- 



328 INTERNAL-COMBUSTION ENGINES 

tures should occur before the end of the compression stroke, so 
that even though the explosion is slow it may be completed near 
the beginning of the working stroke. 

The tests on page 350 show that with the ratio of gas to air 
varying from i :8 to i : 12 the power may vary from 10 to 6 
brake horse-power. 

This discussion of the possibility of varying the power by 
varying the mixture of gas and air would appear to show that 
for many purposes that should be a practicable way of governing 
a gas-engine. Nevertheless it is used very little if at all, although 
it was tried early. 

(2) The common way of governing large gas-engines is to 
vary the supply of the mixture without varying its proportions. 
There are two ways of accomphshing this : in the first place the 
charge may be throttled so that a less weight is drawn in at a 
lower pressure; in the second place the admission valve may be 
closed before the end of the filhng stroke, thus cutting off the 
supply. The effect of throttling is to increase to a marked extent 
the reduction of pressure during the filling stroke with a corre- 
sponding increase in the negative work; the area of the loop 
Hke that shown by Fig. 72, page 313, will increase. The effect 
of closing the inlet-valve before the end of the filling stroke is 
to produce a diagram similar to Fig. 70, page 310. The charge 
is drawn in at a pressure a little below that of the atmosphere 
as far as the point C; then the piston goes on to the end of the 
stroke with an expansion that could be represented by produ- 
cing the curve DC\ the return stroke produces a compression 
that can be represented by retracing the produced part of the 
curve from C and then drawing the true compression curve 
CD. In practice the indicator diagram will show a small nega- 
tive work due to the expansion and compression caused by the 
early closing of the supply-valve, but the loss on that account is 
less than by throtthng. 

(3) The third way of controlling a gas-engine is to cut off 
the gas supply so that the engine draws in a charge of air only 
and makes an idle cycle, represented by Fig. 74, page 323. At 



IGNITION 329 

small power the negative work of idle cycles very much reduces 
the brake economy of the engine. Now, a single-acting four- 
cycle engine has only one working stroke in four, and must fur- 
nish between times the work of expulsion, filling, and compres- 
sion, and even with a very heavy fly-wheel will show an irregu- 
larity in speed of revolution that is very objectionable for many 
purposes. This difficulty is very much increased if the engine 
is governed by omitting explosions on the hit-or-miss principle. 

(4) Delaying ignition is one of the favorite ways of reducing 
the power of automobile-engines on account of its convenience; 
it is little used for other engines, and is very wasteful of fuel, 
as there is not time for proper combustion. 

Ignition. — The ignition of the charge may be produced by 
one of three methods: (i) by an electric spark, (2) by a hot tube, 
or (3) by compression in a hot chamber. 

(i) The electric spark may be produced in one of two ways, 
— by the make-and-break method, or by the jump-spark method. 
For the first method a movable piece is worked inside the cylin- 
der walls, which closes a primary circuit some time before igni- 
tion is desired; the slight closing spark has no effect. At the 
proper time the moving mechanism breaks the circuit, and a 
good spark is made between the terminals, which are tipped 
with platinum. A coil in the circuit intensifies or fattens the 
opening spark. The spark obtained by this method is likely 
to be better than the jump-spark, but there is the great incon- 
venience of a moving mechanism in a cylinder exposed to very 
high pressure, and the motion must be communicated by a 
piece which enters the cylinder through a stuffing-box. 

The jump-spark between two platinum terminals in an insu- 
lated spark-plug, screwed through the cyHnder wall, is a high- 
tension spark in a secondary circuit made by a circuit-breaker 
outside of the cylinder. The movable parts in this case are under 
observation and can be adjusted, and the spark-plug can be 
easily withdrawn for examination or renewal. Frequently there 
are two plugs that can be worked individually or together, or 
both make-and-break and jump-sparks may be supplied. 



330 INTERNAI^COMBUSTION ENGINES 

The circuit may be supplied by a primary battery, or may be 
generated by a small dynamo driven by the engine, or may be 
supplied from any convenient source. When a dynamo is sup- 
plied, the engine is usually started by aid of a battery. 

The electric method of ignition was the earliest used in the 
history of the gas-engine, and though it was at one time neglected, 
now tends to become universal. 

(2) The hot tube requires only a small iron tube, which is 
kept red-hot by a Bunsen burner or other heating flame. The 
tube comes out horizontally from the cyhnder, and sometimes 
is turned upward for convenience in heating. At the proper 
time the explosive mixture in the cylinder is admitted to the 
tube by a valve which is worked by the engine. Sometimes 
the tube has an inlet- valve at the outer end to ventilate the 
tube with air drawn in during the filling stroke. This method 
has been widely used in Great Britain, where the electrical 
method has met with little favor, though the prejudice against 
it is passing away. 

(3) Ignition by compressing the charge in a hot chamber is 
used exclusively in oil-engines, and is an ingenious example of 
taking advantage of a condition that at first sight appears to be 
undesirable. The mixture of air and kerosene oil in engines of 
this class is produced by spraying oil into a chamber attached 
to the cylinder and unprovided with a water-jacket, so that it 
is maintained by the explosion at a red heat. The charge thus 
produced is more likely to be exploded than a mixture of gas 
and air, when it comes in contact w ith a hot surface, and under the 
conditions stated explosion cannot be avoided. Much ingenuity 
has been expended in adjusting sizes and proportions of parts, and 
frequency of explosion, to obtain the explosion when it is desired. 

The tendency to work large gas-engines with high com- 
pression, in order to obtain great power without undue bulk 
and cost, is likely to lead to the danger of premature explosion, 
especially when rich gas is used. Any projecting part (a bolt- 
head or part of a valve) may become sufficiently heated to 
cause explosion; or a spongy spot in a casting may act in the 



GAS-PRODUCERS 



331 



same way. Premature explosion in a small engine after it is 
started may be an inconvenience, but in a large engine it may 
lead to an accident. 

Gas-Producers. — A gas-producer is essentially a furnace 
which burns coal or other fuel with a restricted air supply, so 
that the combustion is incomplete and the products of combus- 
tion are capable of further combustion. In its simplest form a 
gas-producer will deliver a mixture of carbon monoxide and 
nitrogen together with small percentages of carbon dioxide oxygen 
and hydrogen. If a proper proportion of steam is supphed with 
the air, its decomposition in contact with the incandescent fuel 
will yield free hydrogen, and the gas will give a higher pressure 
when exploded, and develop more power in the engine cylinder. 

When gas is produced on a large scale in a stationary plant, 
intricate devices may be used to rectify the gas and save the 
by-products, which are likely to be so important as to control 
the methods employed. The most important by-product at 
the present time appears to be ammonium sulphate, which is 
used as a fertilizer, and for this reason a coal is preferred which 
has a relatively large proportion of nitrogen, x^t a certain 
station a coal containing three per cent of nitrogen produced 
crude ammonium sulphate that could be sold for half the price 
of the coal. This branch of chemical engineering is a specialty 
of growing importance, and an adequate treatment of it would 
demand a separate treatise. Such plants, especially when the 
gas is used for heating furnaces as well as for power, are worked 
under pressure, the air and steam being blown into the furnace. 

When a producer supplies gas for power only, there is a great 
gain in simplicity and in certainty of control, if the producer is 
worked by suction, the engine being allowed to draw its charge 
directly from the producer. During the suction stroke there 
must be a sufficient vacuum in the engine cylinder to work the 
producer; this amounts to about two pounds below the atmos- 
phere. There is no attempt in this case to save by-products, 
and the fuel must be chosen so that comparatively simple rectify- 
ing devices will give a gas that will not clog the engine. At 



332 



INTERNAL-COMBUSTION ENGINES 



the present time the fuels used are coke, anthracite, and non- 
caking bituminous coal. At the Louisiana Purchase Exposi- 
tion, at St. Louis in 1904, a very large variety of fuels, including 
caking bituminous coal and lignite, were used in an experimental 
plant, and it is likely that all kinds of fuel will eventually be 
used in practice. 

Fig. 75 gives the section of a Dowson suction producer, in 
which A is the grate carrying a deep coal fire; at B is the charg- 
ing hopper with double doors, 
so that the vacuum is not lost 
during charging; at C is a 
vaporizer filled with pieces of 
fire-brick, which are heated by 
the hot gases from the furnace; 
water is sprayed on to the fire- 
brick through holes in a circular 
water-pipe D, and flashes into 
steam which mingles with the 
air supply; the air for com- 
bustion enters at F, and passing 
through the vaporizer is charged 
with steam and then flows 
through the pipe L to the ash-pit. In the normal working 
of the engine the gas passes through the pipe G and the 
water-seat at J to the scrubber K, which is filled with coke 
sprayed with water. From K the gas passes directly to 
the engine. To start the producer, kindling is laid on the 
grate and the furnace is filled; the fire is lighted through a 
side door, and air is blown in by a fan driven by hand. At 
first the gas is allowed to escape through the pipe /, until gas 
will burn well at the testing-cock at H; then the pipe / is shut 
off, and the gas is blown through the scrubber and wasted at a 
pipe near the engine until it appears to be in good condition 
when tested at that place. The engine is then started and the 
fan is stopped. 

The producer described is intended to burn coke or anthra- 




FiG. 75- 



OTHER KINDS OF GAS 



333 



cite; those that burn bituminous coal must have some method 
of dealing with tarry matter. Sometimes this is accomplished 
by passing the gas through a sawdust cleaner; sometimes a 
centrifugal extractor is added. Some makers remove the tar 
by care in cooling before the gas comes in contact with water. 
Others pass the distillate through the fire, and thus change it 
into Hght gas or burn it ; with this in view, some producers work 
with a down-draught. It is probable that different kinds of 
fuel will need different treatments. 

Blast-furaace Gas. — From the composition of blast-furnace 
gas on page 316, it is evident that it differs from producer-gas 
only in that it contains very little hydrogen, and therefore is 
hke the gas that would be made in a producer working without 
steam. During the operation of the furnace the composition 
is liable to vary and the gas may become too weak; to remedy 
this difficulty, it is desirable to mingle the gases from two or 
more furnaces. Since the gas available from a furnace may 
be equivalent to 2000 horse-power, it is evident that installations 
to develop power from that source must be on a very large 
scale. 

The gas from a blast-furnace is charged with a large amount 
of dust, some of which is metallic oxide, and readily falls out, 
and the remainder is principally silica and lime which is very 
fine and light. To remove this fine dust the gas should be 
passed through a scrubber, which has the additional advantage 
of cooling the gas. 

Other Kinds of Gas. — Any inflammable gas that can be fur- 
nished with sufficient regularity can be used for developing 
power. The gas from coke-ovens is a rich gas resembling 
producer-gas in its general composition. Natural gas consists 
of 90 to 95 per cent of methane (CH4) with a small percentage 
of hydrogen and nitrogen and traces of other gases. This gas 
for complete combustion requires an equal volume of oxygen 
and consequently about five times its volume of air; it is prob- 
able that ten or twelve volumes of air can be used to advantage 
with this gas in a gas-engine. 



334 INTERNAL-COMBUSTION ENGINES 

Gasoline. — The lighter distillates of petroleum, known as gaso- 
line, are readily vaporized at atmospheric pressure, and provide 
the most ready means of supplying fuel to small engines; engines 
of several hundred horse-power developed in several cylinders 
have been built for small torpedo-boats, but, in general, the use 
of gasoline has been Hmited by its price to comparatively small 
craft and to automobiles; in both cases, whether for pleasure or 
'for business, other things than cost of fuel determine the selec- 
tion of the engines. The same is true for the engines of rela- 
tively small power used for stationary plants. 

The most vital feature of the gasoline-engine is the vaporizer 
or carburetor, and this device has received much attention, 
especially for automobile-engines which are run at very high 
speed. 

There are three types of carburetors that have been used for 
gasoline-engines: (i) those depending on direct vaporization, (2) 
those that depend on aspiration with a float, and (3) those 
depending on aspiration without a float. The earliest types 
depended on direct vaporization as air was drawn through the 
mass of the fluid, or through or over fibrous material or a sur- 
face of wire gauze; some of the latter devices depended on such 
a regulation of feed that nearly all the fluid vaporized as it was 
supplied, leaving only a remnant to return to the tank. But 
in any case there was a chance of fractional vaporization which 
resulted in the production of a heavier and less tractable 
fluid. 

The more recent carburetors depend on aspiration, the air 
supply being drawn past an orifice (or orifices) to which gaso- 
line is supplied, and from which it can be drawn by the air 
more or less in proportion as required. For stationary and 
marine engines the supply of gasoline to the aspirator can be 
nicely regulated by a float which keeps a small chamber filled 
just to the level of the aspirating orifices, so that the inrush of 
air may draw out the gasoline in proper proportion. This 
device has been tried on automobiles, but the shaking of the 
machine disturbs the proper action of the float. 



KEROSENE OIL 



335 



A third form of carburetor is illustrated by Fig. 76. Here 
the gasoline is supplied by a pipe E to a valve that may be set 
to give good average action. Below is a fine conical valve at 
the end of a vertical rod vi^hich is 
held up by a light spring; at the 
middle of the spindle is a disk- 
valve which fit sloosely in a sleeve. 
At aa are air-inlet valves, and at 
A is the entrance to the cylinder. 
During the suction or filling stroke 
the spindle is drawn down, opening 
the valve at the top of the spindle 
and allowing the air to draw 
gasoline by aspiration. Some of 
the hot products of combustion 
from the exhaust are circulated 
around the aspirating chamber to 
prevent undue reduction of tem- 
perature. This type of carburetor 
works well enough at moderate 
speeds, but at very high speeds the inertia of the spindle 
and disk-valve cannot be overcome rapidly enough by the air, 
which is consequently throttled, so that there is not the increase 
of power which might properly be expected at such speeds. 

It is alleged that this type of vaporizer, or carburetor, can be 
made to deal with kerosene oil and alcohol. 

Kerosene Oil. — The use of kerosene oil has been developed 
to the greatest extent in England, on account of former restric- 
tions on the transportation and storage of gasoline. It has 
been used in America where there is objection to gasoline. 

There is much difficulty in vaporizing or spraying kerosene 
oil so that it can be properly mixed with air at the temperature 
for the supply to an engine. On the other hand, any attempt 
to vaporize the oil at a high temperature results in the deposit 
of a hard graphitic material. 

One of the most successful English engineers frankly accepts 
the latter alternative. The essential feature of the carburetor 




Fig. 76. 




336 INTERNAL-COMBUSTION ENGINES 

of this engine is shown in Fig. 77, which gives a vertical section 
of the cylinder- head and of the vaporizer; the remainder of 
the engine differs in no essential particular 
from any horizontal gas-engine. This 
vaporizer, which has a constricted neck, is 
bolted to the cylinder-head; the forward 
end is jacketed with water, as is also the 
cylinder of the engine; but the after end, 
pj^ which is ribbed internally, is not jacketed; it 

consequently remains at a red-heat when 
the engine is running. The oil for each explosion is delivered 
into this hot end of the vaporizer, and is vaporized and mingles 
with the hot spent gases; toward the end of the compression 
stroke the charge of air which has been drawn in and com- 
pressed enters the vaporizer and an explosion occurs. When 
the vaporizer-head has become clogged, after 24 to 200 hours 
running, depending on the kind of oil used, it is taken off and 
the hard adherent deposit is removed; to avoid delay a second 
head is put on for a corresponding run. This engine is 
governed by controlling the oil supply; the governor opens a 
bypass-valve on the oil supply-pipe and allows a part to return 
to the tank. The hit-or-miss principle is not appHcable, as the 
vaporizer would become too cool. Before starting, the vaporizer 
must be heated to a dull red by aid of a kerosene or' gasoline 
torch. The engine can burn also crude petroleum, or an 
unrefined distillate resembling kerosene. 

Alcohol. — The demand for gasoline maintains the price at 
a point which makes it possible in some countries to use alcohol, 
if it can be relieved from special taxation. To make alcohol 
unfit for any but mechanical purposes it is mixed with a little 
wood-alcohol and benzine; this process, called denaturizing, has 
Httle if any effect on its combustion. For combustion the 
amount of water brought over during distillation should be 
limited to a small percentage. The use of alcohol for power in this 
country has only recently been made possible under the internal- 
revenue laws, so that we have no experience with it. There 



THE FOUR-CYCLE ENGINE 



337 



appears to be no reason why there should be trouble in the use 
of some form of carburetor like those used for gasoline engines. 
The Four-cycle Engine. — Fig. 78 gives a vertical section of a 
Westinghouse four-cycle gas-engine built in various sizes, up to 85 
horse- power with one cylinder, and up to 360 with three cylinders. 
Massive engines of this type are horizontal with double- 
acting pistons, having 
two cylinders tandem 
or four twin-tandem. 
It is somewhat curious 
that while massive 
steam-engines tend to- 
wards the upright con- 
struction, large gas- 
engines appear to be 
all horizontal; it may 
be for the convenience 
of the tandem arrange- 
ment. In Fig. 78 the 
frame of the engine is 
arranged to form an 
inclosed crank - case, 
which is somewhat 
unusual for gas- 
engines. The piston 
is in the form of a 
plunger, so that no 
cross-head is needed; 

a common arrangement for all except massive gas-engines. 
The cylinder barrel and head are water- jacketed, the inlet 
and exits being at H and K. Gas and air enter the mixer- 
chamber M by separate pipes (not shown) and pass by N 
to the inlet-valve 7; the engine is controlled by a throttle- valve 
directly connected to a ball-governor beneath the chamber M, 
but omitted from the figure. The valve is a piston-valve 
with separate air and gas passages, which works in a sleeve 




Fig. 78. 



338 INTERNAL-COMBUSTION ENGINES 

that can be moved by hand; this sleeve may be set by hand 
to give any desired mixture, and the proportion of the inlet 
areas for gas and air having been once set, the relative 
areas remain unchanged, while the governor adjusts the 
piston-valve to give the amount of mixture that may be 
demanded by the load on the engine. The inlet-valve / and 
the exhaust-valve E are each moved by cams at B and at A as 
indicated, the cams making one revolution for each double 
revolution of the engine required for the four-stroke cycle. 
Large sizes have the exhaust- valve water-cooled, to prevent 
burning the valve, and to avoid danger of pre-ignition. Near A 
there is a handle for shifting into action the starting-cam which 
reduces compression when the engine is started. At F are two 
low-tension make-and-break ignitors, either of which can be 
thrown into action; they are worked by cams on the shaft that 
operates the valve /. 

Two-cycle Engines. — The two strokes of a four-cycle engine 
which exhaust the spent charge and draw in the new charge are 
performed with a pressure in the cylinder only a little higher or 
lower than that of the atmosphere, and could be omitted with 
advantage provided the operations could be performed in some 
other way. The first successful attempt at a two-stroke cycle 
was that by Dugald Clerk, who made the following changes: 
(i) he cut a ring of exhaust ports through the cyhnder walls that 
were over-run and opened by the piston near the end of the 
expansion stroke, through which the major part of the spent 
gases escaped during release; and (2) he provided a pump set 
about half a stroke ahead of the engine piston, which compressed 
the new charge to about ten pounds above the atmosphere; as 
soon as the exhaust had sufficiently reduced the pressure in the 
cylinder, this new charge opened the inlet-valve and entered the 
cylinder, blowing the remainder of the spent gases out through 
the ports in the cylinder walls. The piston closed these ports 
and compressed the charge on the return stroke, so that only 
two strokes were required to complete the cycle, and the engine 
approximated the condition of a single-acting steam-engine in its 



TWO-CYCLE ENGINES 



339 



regularity of rotative velocity. The engine could also develop 
twice as much power for its size as a four-cycle engine, and in 
certain tests by Mr. Clerk, showed a slightly better economy 
than the older type of engine. But the operation of replacing 
the remnants of the spent charge by the fresh charge in engines 
of this type is rather delicate, there being a chance that some of 
the spent charge will remain, or that some of the fresh charge 
will be wasted; it is likely that the charges mingle and that the 
engine experiences both defects. Eventually the Clerk engine 
was withdrawn from the market, but the principles are used for 
two types of engines: (i) small gasoline engines for launches and 
other small craft, and (2) large engines built for burning blast- 
furnace gas. 

Gasoline-engines of small power and moderate rotative speed 
have been made on the two-cycle principle by enclosing the 
crank- and connecting-rod in a casing, so that the piston may act 
as the compressing-pump. On the up-stroke a charge of air 
and gasoline is drawn into the crank-case, and it is slightly com- 
pressed on the down-stroke. There are two sets of ports cut 
through the cylinder w^alls near the end of the down-stroke and 
are opened by the piston; these are on opposite sides of the 
cylinder; one set, which is opened slightly earlier than the other, 
forms the exhaust-ports and the other the inlet-ports which are in 
communication with the crank-case, and therefore supply air 
and gasoline to replace the spent charge. A barrier is cast on 
the cylinder-head which prevents the fresh charge from flowing 
directly across from the inlet to the exhaust, but nevertheless the 
action is probably much inferior to that of Clerk's engine, which 
had the charge supplied at the cylinder-head. These engines are 
nearly valveless and can run in either direction, and on account 
of the simplicity and small cost have found favor for propelling 
small craft at moderate speeds. 

If any attempt is made to run two-cycle engines at a high 
rotative speed there is difficulty in obtaining proper exhaust 
and supply, since both operations are performed under gaseous 
pressure that cannot well be increased. Recently two-cycle 



340 INTERNAL-COMBUSTION ENGINES 

engines have been introduced on automobiles to a limited extent. 
Two German engineering firms have developed two-cycle engines 
especially for burning blast-furnace gas on a large scale, as much 
as 1500 horse-power in a single cylinder. 

The Korting engine (built by the dc la Verne Machine 
Company) is a double-acting engine which has a piston nearly 
as long as the stroke of the engine. At the middle of the length 
of the cylinder is a ring of exhaust-ports that are uncovered at 
the end of each stroke, and discharge burnt gases from first 
one end of the cylinder and then the other. By the side of the 
engine-cylinder, and arranged in tandem so that they can be 
driven by one crank (which has a lead of 110°), are two pumps, 
one for compressing air, and the other gas. The capacities 
of the two pumps are designed for the kind of gas to be 
burned. 

The air-pump compresses to eight pounds above the atmos- 
phere and delivers air to the admission valves, which are lifted by 
cams at the time when the release is completed. The governor 
controls a bypass-valve which puts the two ends of the 
pump in communication for about half of the discharge 
stroke of that pump, which accomplishes two purposes. In 
the first place the compression of the gas begins only when the 
bypass-valve is closed, and consequently is to a less pressure 
than that of the air; consequently the air backs up in the gas- 
supply pipe, and when the engine admission valve is opened it 
supplies only air which clears the cylinder of spent gases; after- 
ward the cylinder receives its charge of mixed gas and air. By 
careful design and adjustment it is attempted to fill the cylinder 
without wasting gas at the exhaust-ports, but tests show an appre- 
ciable percentage of unburned gas in the exhaust. And in the 
second place the governor can regulate the closure of the bypass- 
valve so as to adjust the amount of gas to the work. Since the 
range of explosive mixture of blast-furnace gas is not wide, this 
method of regulation appears to be adapted only to fairly uni- 
form loads. 

The Oechelhaiiser gas-engine has two single-acting pistons or 



THE DIESEL MOTOR 



341 



plungers in a long open-ended cylinder; these plungers are 
connected to cranks at i8o° so that they approach or recede 
from the middle of the cylinder simultaneously. The engine 
has a cross-head at each end of the cylinder to take the cross- 
thrust of the connecting-rod, so that the engine extends to a 
great length on a horizontal foundation. Toward the crank- 
end of the cylinder there is a ring of exhaust-ports uncovered by 
the inner (or crank-end) piston, and toward the outer end of the 
cylinder there is another row uncovered by the outer piston; a 
part of these outer ports supply air, and a part gas. These air- 
and gas-ports may be controlled by annular valves that are set 
by hand when the engine uses blast-furnace gas. Under these 
conditions the engine is regulated by a governor, which controls 
the pumps that supply air and gas. These pumps, which are 
driven from the outer cross-head, have bypass-valves which 
connect the two ends and begin to deliver only when the 
bypass- valves are shut by the governor, so that the charge is 
adjusted in amount to the load. When the engine uses a rich 
gas that has a wide explosive range, the governor controls the 
annular valves at the gas-ports and varies the mixture. 

The Diesel Motor. — A new form of internal-combustion 
engine was described by Rudolf Diesel in 1893, which does 
away with many of the difficulties 
of gas- and oil-engines, and which 
at the same time gives a much 
higher efficiency. The essential 
feature of his engine consists in 
the adiabatic compression of 
atmospheric air to a sufficient 
temperature to ignite the fuel 
which is injected at a determined 
rate during part of the expansion 
or working stroke. 

The theoretical cycle is shown by 
Fig. 79, which represents four strokes 
of a single-acting piston or plun- 




FlG 



342 



INTERNAL-COMBUSTION ENGINES 



ger. Atmospheric air is drawn in from a to b and is com- 
pressed from Z> to c to a pressure of 500 pounds to the 
square inch and a temperature of 1000° F. From c to d fuel 
is injected in a finely divided form, and as there is air in 
excess it burns completely at a rate that can be controlled 
by the injection mechanism. Thus far the only fuel used 
is petroleum or some other oil. At d the supply of fuel is 
interrupted, and the remainder of the working stroke, de, 
is an adiabatic expansion. The cycle is completed by a release 
at e and a rejection of the products of combustion from b to a. 
The cycle has a resemblance to that of the Otto engine, but 
differs in that the air only is compressed in the cylinder and 
the combustion is accompanied by an expansion. Diesel, in 
his theoretic discussion of his engine, stipulates that the rate 
of combustion shall be so regulated that the temperature shall 
not rise during the injection of fuel, and that the line cd shall 
therefore be very nearly an isothermal for a perfect gas. Since 
the fuel is added during the operation represented by the line 
cd, the weight of the material in the cylinder increases and its 
physical properties change, so that the line will not be a true 
isothermal. The fact that there is air in excess makes it prob- 




FlG. 80. 



able that these changes of weight and properties will be insig- 
nificant. On the other hand, it is not probable that in practice 
the rate of injection of fuel will be regulated so as to give no 



THE DIESEL MOTOR 



343 



rise of temperature, or that there is any great advantage in such 
a regulation if the temperature is not allowed to rise too high. 

The diagram from an engine of this type is shown by Fig. 80, 
which appears to show an introduction of fuel for one-eighth 
or one-seventh of the working stroke. It is probable that the 
compression and the expansion (after the cessation of the fuel 
supply) are not really adiabatic, though as there is nothing but 
dry gas in the cylinder during those operations the deviation 
may not be large. The sides and heads of the cylinders of all 
the engines thus far constructed are water-jacketed, though 
the use of such a water-jacket and the consequent waste of heat 
was one of the difficulties in the use of internal-combustion 
engines that Diesel sought to avoid by controlling the rate of 
combustion. The statement on page 39 that the maximum 
efficiency is attained by adding heat only at the highest tem- 
perature has no application in this case. The real conditions 
are that heat cannot at first be added at a temperature higher 
than that due to compression (about 1000° F.), but as combus- 
tion proceeds heat can be added at higher temperature and 
with greater efficiency. The fuel may be regulated so as to 
avoid temperatures at which dissociation has an influence and 
after-burning can be avoided. 

The oil used as fuel is injected in form of a spray by air that 
is compressed separately in a small pump to 30 or 40 pounds 
pressure above that in the main cylinder; of course it is neces- 
sary to cool this portion of the air after compression to avoid 
premature ignition. The engines that have been used are 
described as giving a clear and nearly dry exhaust. In damp 
weather the exhaust shows a little moisture, probably from the 
combustion of hydrogen in the oil. The cylinder when opened 
shows a slight deposit of soot on the head. It appears there- 
fore that Diesel has succeeded in constructing an engine for 
burning heavy oils with good economy and without the annoy- 
ances of an igniting device. The engines have the further 
advantage in that the work can be regulated by the amount 
of fuel supplied, which amount is not controlled, as in explosive 



344 



NTERNAL-COMBUSTION ENGINES 



engines, by the necessity to form an explosive mixture. The 
discussion of the theoretical efficiency of the cycle shows that 
the efficiency increases as the time of injection of fuel is shortened. 
In practice the engine shows a slight decrease in economy for 
light loads, due probably to the losses by radiation and to the 
water-jacket, which are nearly constant for all loads. 

In the exposition of the theory of his motor, Diesel * claims 
that all kinds of fuel, solid, liquid, and gaseous, can be burned 
in his motor. As yet oil only has been used ; the choice of petro- 
leum or other heavy oil has probably been due to the low cost 
of such oils. It is evident that gas may be used in this type 
of engine; the gas can be compressed separately to a pressure 
somewhat higher than that in the main cylinder, much as the 
air is which is used for injecting oil. It does not appear neces- 
sary to cool the gas after compression, as it will burn only when 
supplied with air. 

There appears to be no insurmountable difficulty in supply- 
ing powdered solid fuel to this engine. The presence of the 
ash from such fuel in the cylinder may, however, be expected 
to give trouble. Diesel claims that with a large excess of air 
(for example, a hundred pounds of air for one pound of coal) 
the ash will be swept out of the cylinder with the spent gases 
and will not give trouble; but that claim has not as yet been 
substantiated. 

Diesel's original discussion of his motor contemplated a com- 
pound compressing-pump, one stage to give isothermal compres- 
sion, and the second stage to give adiabatic compression; also a 
compound motor, the first cylinder having isothermal expansion 
with a supply of fuel, and the second cylinder an adiabatic ex- 
pansion. He gives with that discussion a theoretical diagram 
approaching Carnot's cycle in appearance and efficiency. If 
this variety of the motor were mechanically practicable it would 
have the defects of Carnot's cycle for gas, namely, the diagram 
would be very long and attenuated, and even with the very high 
pressures contemplated would give a relatively small power. 

* Ratiotml Heat Motor ; Rudolf Diesel, trans. Brvan Donkin. 



THE DIESEL MOTOR 



345 



A theoretical discussion of the efficiency of the cycle for the 
simple engine as represented by Fig. 79 may be obtained by 
considering that heat is added at constant temperature from c 
to d and that heat is rejected at constant volume from e to 6, 
bearing in mind that he and dc represent adiabatic changes. 

From equation (75), page 63, the expression for the heat 
supplied from c to d is, for one pound of working substance, 

Q, = Ap^, log.^" = ART, log, J^. 

The heat rejected at constant volume is 

Since the expansion de is adiabatic, 

but since the compression he is also adiabatic, 

and consequenth' 

'-•=-.(;:)■"■(?)■"■-'••©■"■ 

for T'g = Vb. Replacing T^ by its value in the expression for 
Q^, we have 



«--'i-'K?r'--i 

Finally, the efficiency appears to be 



■'■•S ©■"'-■( 



e = Qi ~^^ = I '-^^ '-. (188) 

Inspection of the equation shows that the efficiency may 
be increased by raising the temperature T^ or by reducing the 



346 INTERNAL-COMBUSTION ENGINES 

temperature T^. The latter is practically the temperature of 
the atmosphere, but Tc may be made any desired temperature 
by reducing the clearance of the cylinder and thus raising the 
pressure at the end of compression. Again, the efficienc}- 
may be increased by reducing the time during which fuel is 
injected, that is, by reducing the ratio v^ : v^, as may be proved 
by a series of calculations with different values for that ratio. 
This is a very important conclusion, as it shows that the engine 
will have in practice little if any falling off in efficiency at reduced 
loads. 

It is reported that a clearance of something less than 7 per 
cent is associated with a compression to 500 pounds and a 
temperature of 1000° F., or more. Taking the pressure of 
the atmosphere at 14.7 pounds per square inch, adiabatic com- 
pression to 500 pounds above the atmosphere or to 514.7 pounds 
absolute requires a clearance of 

I T_ 

/ V K y ^ \ 1.405 

^« = -I'b {-A = "^h {-^^^) = 0.0796 vi„ 

so that the clearance is 

0.0796 ^ \i — 0.079 J = 0.0865 

of the piston displacement. 

If the temperature of the atmosphere be taken at 70° F. 
or 530 absolute, the temperature after adiabatic compression 
becomes 

i^ — t I-40S — T 



absolute, or 1020° F. 

If it be further assumed that fuel is supplied for one-tenth 
of the working stroke, then 

T;^ = O.I {Vf, - Va) +Va= [O.I (l - O.O796) + O.O796] T/j 

= O.I 716 Vi,, 



ENGINES FOR SPECIAL PURPOSES 347 

The equation for efficiency gives in this case 

^ = i__ = 0.58. 

1-405 X 53.22 X 1480 loge ^'^^^ 

0.0790 

Engines for Special Purposes. — Small engines can be made 
to give any required degree of regularity for electrical or other 
purposes, by giving a sufficient weight to the fly-wheel; for 
large power the same object can be attained by using a number 
of cylinders, by making the engine double acting, by the con- 
struction of two-cycle engines, or by the combination of two or 
more of these devices. 

The four-cycle engine has not as yet been made reversible, 
and even if the complexity of valve-gear for running in both 
directions could be accepted, it appears likely that a special 
starting device would be required for every reversal. Reversing 
launches and automobiles is done by aid of a mechanical revers- 
ing gear, except that for some small boats a reversing propeller 
is used. Such gear for large ships appears to be dangerous as 
well as impracticable. 

Two-cycle engines would not require much complication of 
valve-gear to make them reversible, and would have some 
advantage on account of the greater frequency of working 
strokes; they also might require the use of a starting gear 
for every reversal. Small launches with two-cycle engines 
are readily reversed by hand, but such small craft can be 
fended off, and a failure to reverse need not be serious. 

The engine with separate compressing-pump discussed on 
page 305, appears to show greater promise for marine or other 
purposes where ready reversal is essential. Even with the 
pump geared directly to the engine, it was found possible to 
reverse a two-cylinder engine promptly with a valve-gear but 
little more complicated than that for a steam-engine. But for 
marine purposes the engines could be placed in two groups ; one 



348 



INTERNAI^COMBUSTION ENGINES 



group could be connected to the propeller shaft (or shafts) and 
worked without compressor-pumps, and the other group at any 
convenient place could drive the compressor- pumps for the 
whole system. Such an arrangement should give practically 
the same certainty of maneuvering as steam-engines. 

The application of gas-engines to large ships cannot be 
considered to be accomplished till producers have been made 
that can use all grades of bituminous coal, including inferior 
qualities. 

Automobiles are commonly driven by four-cycle gasoline 
engines, and have a rather formidable array of mechanical 
devices, including clutches to release the engine for starting, or 
when the carriage is standing still, several change-speed gears 
for running slowly and climbing hills, and a reversing mechanism. 
All of this entails weight, cost and depreciation, and while gaso- 
line vehicles can be handled efficiently by skilled drivers they have 
not the facility of control that is readily given to steam-carriages. 
The speed and power can be controlled by throttling the charge 
and by delaying the ignition; the mixture may be included in 
the methods of control, but probably it is better left alone when 
well adjusted. 

Economy of Gas-Engines. — It will be convenient to consider 
the economy of gas-engines before discussing the economy of 
engines using special fuel like gasoline or oil, because it is only 
this class of engines that can, by association with the gas-producer, 
make use of all kinds of fuel, and especially of coal. 

It will be convenient also to make such inquiry as may be 
possible concerning the influence of various conditions on the 
economy of gas-engines before trying to determine what economy 
may properly be attributed to them. 

There are five conditions that can be enumerated which have 
an effect on the efficiency of gas-engines: 

(i) Compression. 

(2) Mixture. 

(3) Size. 

(4) Quality of gas. 



ECONOMY OF GAS-ENGINES 349 

(5) Time of ignition. 

(i) The influence of compression is indicated theoretically by 
equation (187), page 312, which shows that the efficiency may be 
expected to increase progressively with increasing compression. 
To exhibit this feature and to compare it with the results obtained 
in practice, the following table has been computed for tests 2, 5, 
and 7 of Table XXXV, page 350. The composition of the illumin- 
ating-gas used was similar to that on page 315; the original 
detailed report of these tests shows little variation in composition. 



Number of tests . . 


2 


5 


7 


Ratio of compression 


. 4.98 


4-59 


3.84 


Theoretical efficiency 


. 0.479 


0.461 


0.420 


Thermal efficiency 


. 0.270 


0.264 


0.252 


Ratio 


. 0.564 


0-573 


0.600 



Such a comparison is commonly considered to show that the 
actual efficiency follows the theoretical efficiency, the former 
being based on the indicated horse-power, and being obtained 
by dividing 42.42 (the equivalent of one horse-power in thermal 
units per minute) by the thermal units per indicated horse-power 
per minute. But if the brake horse-power is taken as the basis 
of comparison, as has already been shown to be proper, there 
appears to be practically no advantage in the higher compression 
for the illuminating-gas; for the power-gas there is no advantage 
in a compression beyond four and a half. There is, however, 
an advantage in that a higher compression gives a larger mean 
efifective pressure and greater power. 

(2) A stronger mixture of gas and air may in general be 
expected to yield more work than a weaker one, as is shown b}- 
comparing the trios of tests with the same compression both for 
illuminating-gas and for power-gas; but there is usually some 
mixture that will give the best economy. This mixture should 
be selected from a proper series of engine- tests rather than by 
some other method, but as this involves a large amount of exper- 
imental work, a satisfactory discussion of this feature is not 
always possible. The tests in Table XXXV show that for both 



350 



INTERNAI^COMBUSTION ENGINES 



kinds of gas the richest mixture used is the most economical, 
basing the comparison on brake horse-power as should be done. 
The first trio of tests shows a distinct minimum for a ratio of ten 



Table XXXV. 

GAS-ENGINE WITH ILLUMINATING- AND WITH POWER-GAS. 

DIAMETER 8.6 INCHES; STROKE 1 3 INCHES. 

Professor Meyer, Mitteilungen iiher Forschungsarheiten Heft 8, 1903^ 



















ir. 


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1 

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Is. 
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Mr. 


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4.98 


202 


10.2 


14. 1 


23-2 


8.3 


116 


84 


222 


161 


2 


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.98 


204 


8-3 


12.5 


0.66 


23-8 


10.5 


117 


87 


236 


157 


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98 


204 


6.2 


10. 


0.62 


29.7 


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8.6 


118 


87 


281 


174 


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59 


200 


9-7 


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0.74 


23.2 


102 


87 


224 


166 


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200 


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0.70 


24:0 


IO-5 


105 


88 


229 


161 


6 


S 


4 


59 


202 


6.2 


10.7 


0.58 
0.79 


28.4 


II. 2 
10.9 


108 
82 


89 


281 


162 


7 


3 


84 


207 


10.5 


13-3 


22.9 


86 


213 


168 


ii 




3 


84 


208 


8.5 


12.5 


, 0.68 


24-5 


II. 


89 


87 


252 


170 


9 




3 


84 


207 


6.3 


10. 1 


0.62 


28.0 


11 .1 


89^ 
107 


88 
80 


275 


170 


10 


4 


98 


202 


9.2 


12.6 


0-73 


107-5 


1.05 


251 


181 


11 




4 


98 


294 


^■3 


12.4 


0.67 


II5-5 


1. 18 


107 


80 


247 


164 


12 


CO 


4 


98 


207 


6.2 


9-3 


0.65 


121. 5 


1.78 
I 13 


III 


81 


282 


178 


33 


4 


59 


201 


S.S 


12. 1 


0-73 


108.0 


98 


81 


250 


184 


14 


4 


59 


203 


8.2 


II. 7 


0.70 


121. 5 


1. 12 


lOI 


82 


267 


187 


15 


1 
5 


4 


59 


202 


6.2 


10. 


0.62 


145 


1 .40 
1.20 


lOI 


83 


302 


186 


16 


3 


84 


204 


8.3 


II. 4 


0-73 


124.0 


81 


86 


263 


195 


17 




3 


84 


205 


7-3 


10.4 


0.70 


128.5 


1-39 


82 


85 


275 


194 


18 




3 


84 


205 


(>-3 


9-5 


0.66 


138.0 


1 .64 


81 


85 


292 


190 



to one; the minimum per brake horse-power will be found for a 
richer mixture, on account of the better mechanical efficiency 
which accompanies the larger power which such a mixture will 
develop; it cannot be far wrong to assume that the mixture of 



ECONOMY OF GAS-ENGINES 351 

eight to one will give the minimum per brake horse-power. The 
remainder of the table is less conclusive, but it appears likely 
that a ratio of eight volumes of illuminating-gas to one volume 
of air is proper, and that for power-gas the ratio should be some- 
what larger than unity. 

(3) A committee of the Institution of Civil Engineers * tested 
three gas-engines of varying size, but all having the same ratio 
of compression, and tested under the same conditions. The 
results that bear on the question of size are as follows : 

Brake horse-power 5.2 20.9 52.7 

Thermal units per horse-power per 



ISO 1=^0 14^ 
minute \ jy J ^o 

It is to be remarked that the results just quoted are remarkably 
low, but that the composition of the committee and the precau- 
tions taken, place them beyond cavil. It is somewhat difficult to 
account for the difference between the results just quoted, and 
those given in Table XXXV, though part of it is due to the better 
mechanical efficiency of the former. This was estimated to be 
about 0.87, while that of the engine tested by Professor Meyer 
was about 0.72; allowance for this difference may be estimated 
to reduce the results of the first test in Table XXXV to 184 
thermal units per brake horse-power per minute. This illus- 
trates an inconvenience of using the brake horse-power as the 
basis of comparison of tests on different engines, since it makes 
the results depend on the mechanical condition of the engine; 
however, this condition is one of the elements of practical 
economy. 

(4) It is likely that an engine will show a better heat economy 
when using a richer gas, as is indicated by comparing the results 
in Table XXXV with illuminating-gas and with power-gas; but 
there is not sufficient information to make this feature decisive. 

(5) It is customary to time the ignition so that the maximum 
pressure shall come early in the stroke, and that is probably 
conducive to good economy; delaying ignition, as is done on 
automobiles lo reduce the power, is known to be very wasteful. 

* Proc. Inst. Civ. Engrs., vol. clxii, p. 241. 



352 INTERNAL-COMBUSTION ENGINES 

Professor Meyer made some subsidiary tests to determine 
the influence of the time of ignition on illuminating-gas with the 
results following: 

Lead of ignition, 1.2 5.6 9.7 ii.o 10.9 14.2 20.7 

Thermal units per indi- J 

Gated horse-power per > 216 217 223 216 221 226 260 

minute ) 

This appears to show that any lead up to 15° would give about 
the same result for this engine, but that a greater lead was 
undesirable. 

The question as to the economy to be expected from gas- 
engines has been considered incidentally in our review of the 
influence of various conditions on the economy of gas-engines. 
The best result that is quoted is for an engine tested by the 
committee of the Institution of Civil Engineers, which used 143 
thermal units per horse-power per minute, when developing 52.7 
brake horse-power. The gas used had the composition by 
volume : 

Hydrocarbons ... 4.74 Carbon dioxide . . 2.62 

Methane CH4 ... 33.73 Oxygen 0.27 

Hydrogen ..... 41.29 Nitrogen 10.22 

Carbon monoxide . . 7.13 Total ...... 100 

Its heat of combustion determined by aid of a Junker calori- 
meter was 561 B.T.U. 

The test of a producer gas-power plant at St. Louis given on 
page 354 used 198 thermal units per brake horse-power per 
minute. 

An engine developing 728 metric horse-power at Seraing at 
93 revolutions per minute, used 163 thermal units per brake 
horse-power per minute; the mechanical efficiency being 0.82, 
when tested by Hubert.* 

A Producer- Gas Plant. — At the Louisiana Purchase Exposi- 
tion at St. Louis in 1904, an extensive investigation was made of 
various fuels from all parts of the United States, including the 

* Bui. Soc. de VIndustrie Mineral, 3d series, vol. xiv, p. 1461. 



A PRODUCER-GAS PLANT 



353 



development of power by the combination of a Taylor gas-pro- 
ducer with necessary adjuncts, and a three-cylinder Westinghouse 
gas-engine; a detailed report of the tests is given by Messrs. 
Parker, Holmes, and Campbell,* the committee in charge. 

The gas-producer had a diameter of 7 feet inside the brick 
lining, and at the bottom was a revolving ash table 5 feet in 
diameter; the blast was furnished by a steam-blower supplied 
from a battery of boilers used for other purposes; tests were 
made to determine the probable amount of steam taken by the 
blower, but the variation of steam-pressure acting at the blower 
during tests made this determination somewhat unsatisfactory. 
The cost of the steam in coal of the kind used for any test could 
be estimated closely from boiler-tests made with the same coal. 

The gas from the producer passed through a coke-scrubber, 
and then through a centrifugal tar-extractor using a liberal 
amount of water. From the extractor the gas passed through 
a purifier filled with iron shavings to extract sulphur. On the 
way to the engine the gas was measured in a meter. 

The engine-cylinders were 19 inches in diameter and had 22 
inches stroke. At 200 revolutions the engine was rated at 235 
brake horse-power. The engine was belted to a direct-current 
generator, and the energy was absorbed by a water-rheostat. 

The results of a test on a bituminous coal from West Virginia 
have been selected for presentation. The composition of the 
coal by weight and the gas by volume are: 



Coal. 
Moisture . . . 
Volatile matter 
Fixed carbon . 

Ash 



Thermal units 
per pound coal 



Gas. 

2.22 Carbon dioxide ... 8 

31.05 Carbon monoxide . . 14 

59.83 Oxygen 

6.90 Hydrogen 9 

Methane 6 

[ 14224 Nitrogen 59 



90 

77 
33 
52 
65 

83 



Thermal units per " 
cu. ft. (62° F., I 
14.7 pounds) 

* U. S. Geological Survey, Professional Paper No. 48. 



160.5 



354 INTERNAL-COMBUSTION ENGINES 

Test on Producer and Engine. 

Duration, hours 24 

Total coal fired in producer, pounds 6,000 

Coal equivalent of steam used by blower, pounds 835 

Coal equivalent of power to drive auxiliary machinery 299 

Total equivalent coal 7, 134 

Thermal value of total, equivalent coal, b.t.u. 101,500,000 

Total gas (at 62° F. and 14.7 pounds), cu. ft 415,660 

Thermal value of total gas 66,700,000 

Efficiency of producer 0657 

Electrical horse-power i99-3 

Mechanical efficiency, estimated o . 85 

Brake horse-power 234 

Gas per horse-power per hour, cubic feet . . . . ' 74.1 

Thermal units per horse-power per minute 198 

Thermal efficiency of brake-power 0.214 

Coal per brake horse-power per hour 1.27 

Combined thermal efi&ciency of producer and engine 0.14 

It is interesting to compare these results of a test on a producer- 
plant with the tests at the pumping-station at Chestnut Hill 
from which the results quoted on page 239 were taken. 

Test at Chestnut Hill Pumping Station. 

Duration hours, ' 24 

Coal required by plant, corrected 16,269 

Thermal value of George's Creek coal, estimated 14,500 

Heat abstracted from one pound of coal by boiler 10,690 

^Efi&ciency of boiler o . 74 

Indicated horse-power, engine 576 

Indicated horse-power, pump 530 

Mechanical efi&ciency 0.920 

Thermal units per pump horse-power per minute 222 

Thermal efi&ciency pump-power 0.191 

Combined thermal efi&ciency pump and boiler 0.14 

Coal per pump horse-power per hour 1.21 

If allowance is made for the higher thermal value of George's 
Creek coal, the coal consumptions are very nearly equivalent. 

A test on a Dowson suction producer by Mr. M. A. Adam * 
gave an efficiency of 0.80 to 0.84 after the producer was well 
started. If the thermal efficiency of an engine using the gas 
may be estimated from 0.20 to 0.24, the combined efficiency may 
be estimated from 0.16 to 0.20, which for anthracite coal would 

* Proc. Inst. Civ. Engrs., vol. clviii, p. 320. 



ECONOMY OF A DIESEL MOTOR 



355 



correspond to one pound per brake horse-power per hour, or 0.9 
of a pound per indicated horse- power; the makers of producer 
power-plants are now ready to guarantee a consumption of 
one pound of anthracite per brake horse-power per hour. 

Economy of Oil- Engine. — An engine of the type described on 
page 335 was tested by Messrs. A. E. Russell and G. S. Tower * 
of the Massachusetts Institute of Technology. The engine 
had a diameter of 11.22 inches and a stroke of 15 inches, and at 
220 revolutions per minute developed ten brake horse-power; 
the mechanical efficiency was about 0.72, so that the indicated 
power was about 14; the clearance or charging space was about 
0.44 of the piston displacement. 

With kerosene the best economy was 1.5 pounds per brake 
horse-power per hour; this kerosene weighed 6.52 pounds 
per gallon, flashed at 104° F., and had a calorific power of 
17,222 thermal units per pound. 

The engine was also tested with a crude distillate which 
comes from petroleum after the kerosene, weighing 6.66 pounds 
per gallon, with a flash-point at 148° F., and having a calorific 
power of 19,410 thermal units per pound; of this oil the engine 
used 1.3 pounds per brake horse-power per hour. 

The thermal units per horse-power per minute were 430 for 
kerosene and 420 for the distillate; the thermal efficiencies corre- 
sponding are 0.099 ^^^ o.ii on the basis of brake horse-power. 

Economy of a Diesel Motor. — A 70 horse-power Diesel 
motor using Russian petroleum, which had a calorific power of 
18,450 thermal units per pound, was tested by Professor Meyer f 
in 1904. The diameter of the cylinder was 15.75 inches, the 
stroke was 23.7 inches, and the ratio of compression was 15.4. 
The air-pump had a diameter of 2.2 inches and a stroke of 5.5 
inches. At the normal load of 69.63 metric horse-power by the 
brake (68.6 English horse-power) the oil-consumption was 0.429 
pound per horse-power per hour, or 132 thermal units per brake 
horse-pov/er per minute. The thermal efficiency was conse- 

* Thesis, M. I .T. 1905. 

t Mitteilungen uber Forschungsarbeiten Heft 17, p. 35. 



356 



INTERNAI^COMBUSTION ENGINES 



quently 0.32. At an overload amounting to 85.7 brake horse- 
power, the oil-consumption was 0.42 pound, and at half load 
(34.4 horse-power) the consumption was 0.50 of a pound. 

Since oil for lubrication of the cylinder is liable to be burned 
together with the fuel, it is specially necessary in tests of engines 
of this type that error from the effect of excessive use of lubri- 
cating-oil is to be guarded against. 

Distribution of Heat. — A very interesting and instructive 
matter in the discussion of tests on gas-engines is the distribution 
of the heat, and especially of the heat that is not changed into 
work. It cannot be considered that all of this lost heat is wasted, 
because any heat-engine must reject heat, and that for the theo- 
retical cycles, which are the limits for practical engines, the 
major part of the heat is unavoidably rejected. 

The following table is taken from a lecture by Mr. Dugald 
Clerk.* 



Dimension 


Distribution of Heat. 


of Engine. 


Work. 


Jacket. 


Exhaust. 


6.75 X 13.7 

9.5 X 18.0 

26 X 36 ^ 

2 cyls. S 

51.2 X 55.13 


0.16 
0.22 

0.28 

0.28 


0.51 

0.43 
0.24 
0.52 


0.31 

0-35 

0.59 
0.20 



The first three show, together with a notable gain in efficiency, 
a strong tendency to shift the waste heat from the water-jacket 
to the exhaust, as the engine increases in size; the last test is 
from an engine using blast-furnace gas, and which is liberally 
cooled with water. The whole table, and especially the last 
two examples, show that to a large extent an engineer may decide 
in the design of an engine, whether he will withdraw heat by 
thorough cooling, or allow the heat to be suppressed by disso- 
ciation and thrown out in the exhaust. 

Mean Effective Pressure. — In the design of a gas-engine the 

* Forest Lecture. Inst. Civ. Eng. cxliii. p. 21. 



WASTE-HEAT ENGINES 357 

first question to be determined is the mean effective pressure 
that is desired or can be obtained. This must depend on the 
fuel and its mixture with air, and on the degree of compression. 
There does not at the present time appear to be information 
that will serve as the basis of a working theory for determining 
the mean effective pressure even when these features are 
determined. 

It is desirable, in order that the engine shall be powerful and 
compact, that the mean effective pressure shall be high; English 
engineers commonly make use of 90 to 100 pounds mean effective 
pressure; but German engineers who have had experience with 
very large engines for which pre- ignition is dangerous, have been 
content with 60 pounds or less. 

Waste-heat Engines. — On page 180 attention was called to 
the fact that the exhaust-steam from a steam-engine could be 
used for vaporizing some fluid like sulphur dioxide, and that 
thereby the temperature range could be extended. The only 
tests quoted failed to show the advantage that might be expected 
when this method is used with steam-engines. But the exhaust 
from a gas-engine is very hot, probably 1000° F., or over, and 
there appears to be no reason why the heat should be wasted, 
as it could readily be used to form steam in a boiler or for other 
purposes. 



CHAPTER XV. 

COMPRESSED AIR. 

Compressed air is used for transmitting power, for storing 
energy, and for producing refrigeration. Air at moderate 
pressure, produced by blowing-engines, is used in the production 
of iron and steel; and currents of air at slightly higher pressure 
than that of the atmosphere (produced by centrifugal fan- 
blowers) are used to ventilate mines, buildings, and ships, and 
for producing forced draught for steam-boilers. Attention will 
be given mainly to the transmission and storage of energy. The 
production and use of ventilating currents require and are sus- 
ceptible of but little theoretical treatment. Refrigeration will 
be reserved for another chapter. 

A treatment of the transmission of power by compressed air 
involves the discussion of air-compressors, of the flow of air 
through pipes, and of compressed-air engines or motors. The 
storage of energy differs from the transmission of power in that 
the compressed air, which is forced into a reservoir at high 
pressure, is used at a much lower pressure at the air- motor. 

Air-Compressors. — There are three types of machines used 
for compressing or moving air: (i) piston air-compressors> (2) 
rotary blowers, (3) centrifugal blowers or fans. 

The piston air-compressor is always used for producing high 
pressures. It consists of a piston moving in a cylinder with 
inlet- and exit-valves at each end. Commonly the valves are 
actuated by the air itself, but some compressors have their valves 
moved mechanically. Blowing-engines are usually piston- 
compressors, though the pressures produced are only ten or 
twenty pounds per square inch. 

Rotary blowers have one or more rotating parts, so arranged 
that as they rotate, chambers of varying capacity are formed, 

358 



FLUID PISTON-COMPRESSORS 



359 



which receive air at atmospheric pressure, compress it, and 
deliver it against a higher pressure. They are simple and com- 
pact, but are wasteful of power on account of friction and leakage, 
and are used only for moderate pressures. 

Fan-blowers consist of a number of radial plates or vanes, 
fixed to a horizontal axis and enclosed in a case. When the 
axis and the vanes attached to it are rotated at a high speed, air 
is drawn in through openings near the axis and is driven by 
centrifugal force into the case, from which it flows into the 
delivery-main or duct. Only low pressures, suitable for ventila- 
tion and forced draught, can be produced in this way. But 
little has been done in the development of the theory or the 
determination of the practical efficiency of fan-blowers. Some 
ventilating-fans have their axes parallel to the direction of the 
air-current, and the vanes have a more or less helicoidal form, 
so that they may force the air by direct pressure; they are in 
effect the converse of a windmill, producing instead of being 
driven by the current of air. They are useful rather for moving 
air than for producing a pressure. 

Fluid Piston- Compressors. — It will be shown that the effect 
of clearance is to diminish the capacity of the compressor; con- 
sequently the clearance should be made as small as possible. 
With this in view the valves of compressors and blowers are 
commonly set in the cylinder-heads. Single-acting compressors 
with vertical cylinders have been made with a layer of water or 
some other fluid on top of the piston, which entirely fills the 
clearance-space when the piston is at the end of the stroke. An 
extension of this principle gives what are known as fluid piston- 
compressors. Such a compressor commonly has a double-acting 
piston in a horizontal cylinder much longer than the stroke of 
the piston, thus giving a large clearance at each end. The 
clearance-spaces extend upward to a considerable height, and the 
admission- and exhaust- valves are placed at or near the top, and 
the entire clearance-space is filled with water. The spaces 
and heights must be so arranged that when the piston is at one 
end of its stroke the water at that end shall fill the clearance 



360 COMPRESSED AIR 

and cover the valves, and at the other end the water shall not 
fall to the level of the top of the cylinder. There are conse- 
quently two vertical fluid pistons actuated by a double-acting 
horizontal piston. It is essential that the spaces in which the 
fluid pistons act shall give no places in which air may be caught 
as in a pocket, and that there are no projecting ribs or other 
irregularities to break the surface of the water; and, further, 
the compressor must be run at a moderate speed. The water 
forming the fluid pistons becomes heated and saturated with 
air by continuous use, and should be renewed. 

Air-pumps used with condensing-engines or for other purposes 
may be made with fluid pistons which are renewed by the 
water coming with the air or vapor. In case the water thus 
supplied is insufficient, water from without may be admitted, 
or water from the delivery may be allowed to flow back to 
the admission side of the pump. 

Displacement Compressors. — When a supply of water under 
sufficient head is available, air may be compressed in suitably 
arranged cylinders or compressors by direct action of the water 
on air, compressing it and expelling it by displacement. Such 
compressors are very wasteful of power, and in general it is 
better to use water-power for driving piston-compressors, prop- 
erly geared to turbine- wheels or other motors. 

Cooling during Compression. — There is always a considerable 
rise of temperature due to compressing air in a piston air-com- 
pressor, which is liable to give trouble by heating the cylinder 
and interfering with lubrication. Blowing-engines which pro- 
duce only moderate pressures usually have their cylinders lubri- 
cated with graphite, and no attempt is made to cool them. All 
compressors which produce high pressures have their cylinders 
cooled either by a water-jacket or by injecting water, or by 
l)oth methods. 

Since the air after compression is cooled either purposely or 
unavoidably, there would be a great advantage in cooling the 
air during compression, and thereby reducing the work of com- 
})ression. Attempts have been made to cool the air by spray- 



MOISTURE IN THE CYLINDER 361 

ing water into the cylinder, but experience has shown that the 
work of compression is not much affected by so doing. The 
only effective way of reducing the work of compression is to 
use a compound compressor, and to cool the air on the way 
from the first to the second cylinder. Three-stage compressors 
are used for very high pressures. It is, however, found that 
air which has been compressed to a high pressure and great 
density is more readily cooled during compression. 

Moisture in the Cylinder. — If water is not injected into the 
cylinder of an air-compressor the moisture in the air will depend 
on the hygroscopic condition of the atmosphere. But even if 
the air were saturated with moisture the absolute and the rela- 
tive weight of water in the cylinder would be insignificant. 
Thus at 60° F. the pressure of saturated steam is about one- 
fourth of a pound per square inch, and the weight of one cubic 
foot is about 0.0008 of a pound, while the weight of one cubic 
foot of air is about 0.08 of a pound. It is probable that the 
only effect of moisture in the atmosphere is to slightly reduce 
the exponent of the equation (77), page 64. This conclu- 
.sion probably holds when the cylinder is cooled by a water- 
jacket. 

When water is sprayed into the cylinder of a compressor 
the temperature of the air and the amount of vapor mixed with 
it vary, and there is no ready way of determining its condition. 
But, as has been stated, the spraying of water into the cylinder 
does not much reduce the work of compression, and consequently 
it is probable we can assume that the compression always fol- 
lows the law expressed by an exponential equation; such as 

The value to be given to n is not well known; it may be as 
small as 1.2 for a fluid piston-compressor, and it may approach 
1 .4 when the cooling of the air is ineffective, as is usually the case. 

Power Expended. — The indicator-diagram of an air-com- 
pressor with no clearance-space is represented by Fig. 81. Air 
is drawn in at atmospheric pressure in the part of the cycle 



362 



COMPRESSED AIR 




of operations represented by dc) in the part represented by ch 
the air is compressed, and in the part represented by ha it is 
expelled against the higher pressure. 

If p^ is the specific pressure and v^ the 
specific volume of one pound of air at atmos- 
pheric pressure, and p^ and v^ corresponding 
quantities at the higher pressure, then the 

Fig. 81. 

work done by the atmosphere on the piston 
of the compressor while air is drawn in is p^v^. Assuming 
that the compression curve ch may be represented by an expo- 
nential curve having the form 

pv"" = p^v^ = const., 

then the w^ork of compression is 



_ii 



^ MA 

n- i\ \pj 
The work of expulsion from 6 to a is 



p.v^-pM^-p.vM'^ 



The effective work of the cycle is therefore 

n — 1 

Equation (189) gives the work done to compress one pound 
of air, p^ and p^ being specific pressures (in pounds per square 
foot), and v^ the specific volume, which may be calculated by 
aid of the equation 

T r/ 



EFFECT OF CLEARANCE 363 

in which the subscripts refer to the normal properties of air at 
freezing-point and at atmospheric pressure. 

If, instead of the specific volume i/^, we use the volume V^ of 
air drawn into the compressor we may readily transform equation 
(189) to give the horse-power directly, obtaining 

H.P.= i44/>.F,. (/m""^_ ) 
S300o(n - i) l\pj S 

where p^ is the pressure of the atmosphere in pounds per square 
inch, and n is the exponent of the equation representing the 
compression curve, which may vary from 1.4 for dry-air com- 
pressors to 1.2 for fluid piston-compressors. 

Effect of Clearance. — The indicator-diagram of an air- 
compressor with clearance may be represented by Fig. &2. 
The end of the stroke expelling air is at a, 
and the air remaining in the cylinder ex- 
pands from a to d, till the pressure becomes 
equal to the pressure of the atmosphere 
before the next supply of air is drawn in. "^ "f^ZIZ" 
The expansion curve ad may commonly be 
represented by an exponential equation having the same expo- 
nent as the compression curve cb, in which case the air in the 
clearance acts as a cushion which stores and restores energy, 
but does not affect the w^ork done on the air passing through the 
cylinder. The work of compressing one unit of weight of air 
in such a compressor may be calculated by aid of equation 
(189), but the equation (190) for the horse- power cannot be used 
directly. 

The principal effect of clearance is to increase the size of the 
cylinder required for a certain duty in the ratio of the entire 
length of the diagram in Fig. 82 to the length of the line dc. 

Let the clearance be — part of the piston displacement. At 

m 

the beginning of the filling stroke, represented by the point a, 
that volume will be filled with air at the pressure p^. After the 
expansion represented by ad the air in the clearance will have 



a 

I 


b 

^ — « 




1 



364 COMPRESSED AIR 

the pressure p^y and, assuming that the expansion follows the 
law expressed by the exponential equation 

P'v'' = ^i^i" (190a) 

its volume will be 






m 

part of the piston displacement. The ratio of the line dc to the 
length of the diagram will consequently be 

1 

ac m \p^i 



-=x-lgA%l (X9X) 

m\pj m 



and this is the factor by which the piston displacement calculated 
without clearance must be divided to find the actual piston 
displacement. 

Temperature at the End of Compression. — When the air in 
the compressor-cylinder is dry or contains only the moisture 
brought in with it, it may be assumed that the mixture of air and 
vapor follows the law of perfect gases, 

PV_^ pj^Vi 

T T^ ' 
which, combined with the exponential equation 

pv^=p,v,\ 
gives 

n—\ 

from which the final temperature T^ at the end of compression 
may be determined when T^ is known. When water is used 
freely in the cylinder of a compressor the final temperature 
cannot be determined by calculation, but must be determined 
from tests on compressors. 

Contraction after Compression. — Ordinarily compressed air 
loses both pressure and temperature on the way from the com- 



VOLUME OF THE COMPRESSOR CYLINDER 365 

pressor to the place where it is to be used. The loss of pressure 
will be discussed under the head of the flow of air in long pipes ; 
it should not be large, unless the air is carried a long distance. 
The loss of temperature causes a contraction of volume in two 
ways : first, the volume of the air at a given pressure is directly 
as the absolute temperature; second, the moisture in the air 
(whether brought in by the air or supplied in the condenser) in 
excess of that which will saturate the air at the lowest temperature 
in the conduit, is condensed. Provision must be made for 
draining off the condensed water. The method of estimating 
the contraction of volume due to the condensation of moisture 
will be exhibited later in the calculation of a special problem. 

Interchange of Heat. • — The interchanges of heat between 
the air in the cylinder of an air-compressor and the walls of the 
cylinder are the converse of those taking place between the steam 
and the walls of the cylinder of a steam-engine, and are much 
less in amount. The walls of the cylinder are never so cool as 
the incoming air, nor so warm as the air expelled; consequently 
the air receives heat during admission and the beginning of 
compression, and yields heat during the latter part of com- 
pression and during expulsion. The presence of moisture in 
the air increases this effect. 

Volume of the Compressor Cylinder. — Let a compressor 
making n revolutions per minute be required to deliver Fg cubic 
feet of air at the temperature t^ F., or 7^3° absolute, and at the 
absolute pressure p^ pounds per square inch, at the place where 
the air is to be used. Assuming that the air is dry when it is 
delivered and that the atmosphere is dry when it is taken into 
the compressor, then the volume drawn into the compressor per 
minute at the temperature T^ and the pressure p^ will be 

^1= ^af^^ (193) 

cubic feet; and this expression will be correct whatever may be 
the intermediate temperatures, pressures, or condition of satura- 
tion of the air. 



366 



COMPRESSED AIR 



If the compressor has no clearance the piston displacement 
will be 

-f (194) 

if the clearance is — part of the piston displacement, dividing 
fn 

by the factor (191) gives for the piston displacement 



2W 



expressed in cubic feet. , 

The pressure in the compressor-cylinder when air is drawn 
in, is always less than the pressure of the atmosphere, and when 
the air is expelled it is greater than the pressure against which 
it is delivered. From these causes and from other imperfections 
the compressor will not deliver the quantity of air calculated 
from its dimensions, and consequently the volume of the cylinder 
as calculated, whether with or without clearance, must be in- 
creased by an amount to be determined by experiment. 

Compound Compressors. — When air is to be compressed 
from the pressure p^ to the pressure p^, but is to be delivered at 
the initial temperature t^, the work of compression may be 
reduced by dividing it between two cylinders, one of which 
takes the air at atmospheric pressure and delivers it at an 
intermediate pressure p' to a reservoir, from which the other 
cylinder takes it and delivers it at the required pressure p^, 
provided that the air be cooled, at the pressure p', between the 
two cylinders. 

The proper method of dividing the pressures and of pro- 
portioning the volumes of the cylinders so that the work of 
compression may be reduced to a minimum may be deduced 
from equation (189) when there is no clearance or when the 
clearance is neglected. 



COMPOUND COMPRESSOR 367 

The work of compressing one pound of air from the pressure 

p^ to the pressure p' is 

» — 1 

^•-^•^';rhKA)"-4 • • • • ^'''^ 

The work of compressing one pound from the pressure f to p^ 
is 

because the air after compression in the first cylinder is cooled 
to the temperature t^ before it is supplied to the second cylinder, 
and consequently fv' = p^v^. The total work of compression is 

n — 1 n — 1 

and this becomes a minimum when 

n — 1 n — 1 



w. 



if) ' -e-) 



becomes a minimum. Differentiating with regard to p^, and 
equating the first differential coefficient to zero, gives 

/ = ^pj2 (199) 

Since the air is supplied to each cyHnder at the temperature t^, 
their volumes should be inversely as the absolute pressures p^ 
and p'. This method also leads to an equal distribution of work 
between the two cylinders, for if the value of p' from equation 
(189) is introduced into equations (197) and (198) we shall 
obtain 



n — l 

2n 



W^^W, = p^v,^^\(^j "-.j. . .(300) 

and the total work of compression is 

w — 1 



368 COMPRESSED AIR 

Three-Stage Compressors. — When very high pressures are 
required, as where air is used for storing energy, it is customary 
to use a compressor with a series of three cyHnders, through 
which the air is passed in succession, and to cool the air on the 
way from one cylinder to the next. If the initial and final pres- 
sures are p^ and p^, and if f and p" are the pressures in the 
intermediate receivers in which the air is cooled, the conditions 
for most economical compression may be deduced in the follow- 
ing way: 

The work of compressing one pound of air in the several 
cylinders will be 

n — 1 



W, 



^'""'^Aij) "-i • ■ • -(-4) 

But since the air is cooled to the initial temperature on its way 
from one cylinder to the other so that 

p^v^ = p'v' = p"v"\ 
the total work of compressing one pound of air will be 

This expression will be a minimum when 

n — 1 n — 1 n — 1 

becomes a minimum; that is, when 



J 

hk n - 1 f "" n - 1 p' 



pr P' ' 



= o . . (206) 



FRICTION AND IMPERFECTIONS 369 

and _L "-1 

= r — ^ — ^ = o . , . (207) 

Equations (206) and (207) lead to 

f' = p^f^ ....... (208) 

p'^'-^fp, ....... (209) 

from which by eUmination we have 

/ = ^J^, • .(210) 

and , 

P" =^P.P.' •...».. (211) 
Since the temperature is the same at the admission to each 
of the three cylinders, the volumes of the cylinders should be 
inversely proportional to the absolute pressures p^^ f, and p'' . 
As w^ith the compound compressors, this method of arranging 
a three-stage compressor leads to an equal distribution of work 
between the cylinders. For, if the values of f and f' from 
equations (210) and (211) are introduced into equations (202) to 
(204), taking account also of the equation (190a) we shall have 

n — \ 

W,= W._ = W,= p,v, ^ j (^^) " - I j . (212) 
and consequently the total work of compression is 

n — \ 

Friction and Imperfections. — The discussion has thus far 
taken no account of friction of the compressor nor of imperfec- 
tions due to delay in the action of the valves and to heating the 
air as it enters the cyHnder of the compressor. 

From comparisons of indicator-diagrams taken from^ the 
steam- and the air-cylinders of certain combined steam-engines 
and air-compressors at Paris, Professor Kennedy found a mechan- 
ical efficiency of 0.845. Professor Gutermuth found an efficiency 
of 0.87 for a new Riedler compressor. It will be fair to assume 
an efficiency of 0.85 for compressors which are driven by steam- 



370 



COMPRESSED AIR 



engines; compressors driven by turbines will probably be affected 
to a like extent by friction. 

The following table given by Professor Unwin * shows the 
effect of imperfect valve-action and of heating the entering air 
as deduced from tests on a Dubois- Francois compressor which 
had a diameter of i8 inches and a stroke of 48 inches. 



RATIO OF ACTUAL AND APPARENT CAPACITIES OF AN 
AIR-COMPRESSOR. 







Ratio of air 






delivered at 


Piston speed, 
feet per 
minute. 


Revolutions 


atmospheric 
pressure and 


per minute. 


temperature to 
volume dis- 






placed by 






piston. 


80 


10 


0.94 


160 


20 


0.92 


200 


25 


0.90 


240 


30 


0.86 


280 


35 


0.78 



This table does not take account of the effect of clearance, 
nor is the clearance for the compressor stated. It is probable 
that five or ten per cent will be enough to allow for imperfect 
valve-action after the effect of clearance is properly calculated. 
The effect of clearance is to require a larger volume of cylinder 
than would be needed without clearance. The effect of imper- 
fect valve-action and of heating of the entering air is to require 
an additional increase in the size of the cylinder of the air-com- 
pressor and also to increase the work of compression. 

Efficiency of Compression. — If air could 
be so cooled during compression that the tem- 
perature should not rise, the compression line 
cb, Fig. 83, would be an isothermal line, 
Fig. 83. and the work of compressing one pound of air 

* Development and Transmission of Power, p. 182. 




EFFICIENCY OF COMPRESSION 



371 



would be 



^ = p2'^2 + Pi'^i log, 



Pi'^i'^^ 



but p^v^ = p^y^ for an isothermal change, and consequently 



W = p,v, log, {^ 
Pi 



(214) 



Some investigators have taken the v^^ork of isothermal com- 
pression, represented by equation (214), as a basis of comparison 
for com^pressors, and have considered its ratio to the actual work 
of compression as the efficiency of compression. This throws 
together into one factor the effect of heating during compression 
and the effect of imperfect valve-action. 

Professor Riedler * obtained indicator-diagrams from the 
cylinders of a number of air-compressors and drew upon them 
the diagrams which would represent the work of isothermal 
compression, without clearance or valve losses. A comparison 
of the areas of the isothermal and the actual diagrams gave the 
arbitrary efficiency of compression just described. The following 
table gives his results: 

ARBITRARY EFFICIENCY OF COMPRESSION. 



Type of compressor. 


Pressures in 

main, 
atmospheres. 


Lost work in 

per cent of 

useful work. 


Arbitrary 
efficiency. 


CoUadon, St. Gothard 

do. 

Sturgeon 

Colladon 

Slide-valve 


6 
6 
3 
4 

5 
6 
6 
6 


• 105 -o 
92.0 

94-3 

38.15 

49-3 

42.7 

40.2 

12.07 


0.488 
0.521 

0.515 
0.772 
0.670 
0.701 

0.713 
0.892 


Paxman 

Cockerill 

Riedler two-stage 



A similar comparison for a fluid piston-compressor showed 
an efficiency of 0.84. 

* Development and Distribution of Power, Unwin. 



372 



COMPRESSED AIR 



There are three notable conclusions that may be drawn from 
this table: (i) there is much difference between compressors 
working at the same pressures, (2) a simple compressor loses 
efficiency rapidly as the pressure rises, and (3) the compound 
or two-stage compressor shows a great advantage over a simple 
compresson. 

Test of a Blowing-Engine. — Pernolet * gives the following 
test of a blowing-engine used to produce the blast for Bessemer 
converters at Creusot. The engine was a two-cylinder horizontal 
engine, with the cranks at right angles. The piston -rod for 
each cylinder extended through the cylinder-head and actuated 
a double-acting compressor. The dimensions were: 

Diameter, steam-pistons 47J inches 

" air-pistons 59 " 

Stroke 70-9 " 

Diameter of fly-wheel 26 i feet 

At 28 revolutions per minute the following results were 
obtained : 

Indicated horse-power of steam-cylinders .... 1078 

" " " air-cylinders 986 

Efficiency 0.92 

Temperature of air admitted 50° F. 

" '' delivered 140° F. 

Pressure of air delivered, pounds per square 

inch gauge 23.4 

Pressure of air in supply-pipe, pounds per 

square inch gauge 0.44 

At 25 revolutions there was no sensible depression of pressure 
in the supply-pipe. 

The air from such a blowing-engine probably suffers little 
loss of temperature after compression. 

Hydraulic Air-Compressor. — The Taylor hydraulic air-com- 
pressor makes use of water-power for compressing air at constant 

* L'Air Comprime, 1876. 



HYDRAULIC AIR-COMPRESSOR 



373 



temperature. The essential features are an aspirator for charg- 
ing the water with air, a column of water to give the required 
pressure, and a separator to gather the air from the water after 
compression. The water is brought to the compressor in a pen- 
stock, as it would be to a water-wheel, and below the dam it flows 
away in a tailrace; the power available is determined from the 
weight of water flowing and the head in the penstock above the 
tailrace, in the usual manner. Below the dam a shaft is exca- 
vated to a depth proper to give the required pressure (about 
2.3 feet depth per pound pressure), and then a chamber is exca- 
vated to provide space for the separator. In the shaft is a 
plate- iron pipe or cylinder, down which the water flows; after, 
passing the separator the water ascends in the shaft and flows 
away at the tailrace. 

The head of the pipe is surrounded by a vertical plate-iron 
drum into which the penstock leads, so that water is supplied 
to the head all round the periphery. The head itself is formed 
of two inverted conical iron-castings, so formed that the space 
into which the water flows at first contracts and then expands; 
the changes of velocity being gradual, no appreciable loss of 
energy ensues. At the throat of the inlet, where the velocity is 
highest, there is a partial vacuum, and air is admitted through 
numerous small pipes so that the water is charged with bubbles 
of air. The upper conical casting can be set by hand to control 
the supply of water and air. 

As the mingled column of water and air-bubbles goes down 
the pipe, the air is compressed at appreciably the temperature 
of the water. At the lower end, the pipe expands to reduce the 
velocity, and delivers the air and water into a plate-iron bell; 
the air gathers in the top of the bell, from which it is led by 
a pipe, and the water escapes under the edge of the bell. Air 
in solution is unavoidably lost, and forms the chief source of 
loss of power in the device. The air is, of course, saturated with 
moisture at the temperature of the water, but that is probably 
the , condition of compressed air however produced. The 
efficiency of the compressor may be taken as about 0.60 to 



374 COMPRESSED AIR 

0.70; making allowance for loss in transmission and for the 
efficiency of the compressed-air motors, the system appears to 
be inferior to the ordinary turbine water-wheel. 

Air-Pumps. — The feed-water supplied to a steam-boiler 
usually contains air in solution, which passes from the boiler 
with the steam to the engine and thence to the condenser. In 
like manner the injection- water supplied to a jet-condenser 
brings in air in solution. Also there is more or less leakage of 
air into the cylinder communicating with the condenser and 
into the exhaust-pipe or the condenser itself. An air-pump 
must therefore be provided to remove this air and to maintain 
the vacuum. The air-pump also removes the condensed steam 
from a surface-condenser, and the mingled condensed steam and 
injection-water from a jet-condenser. If no air were brought 
into the condenser the vacuum would be maintained by the con- 
densation of the steam by the injection, or the cooling water, 
and it would be sufficient to remove the water by a common 
pump, which, with a surface-condenser, might be the feed- 
pump. 

The weight of injection-water per pound of steam, calculated 
by the method on page 149, will usually be less than 20 pounds, 
but it is customary to provide 30 pounds of injection -water per 
pound of steam, with some method of regulating the quantity 
delivered. 

It may be assumed that the injection- water will bring in with 
it one-twentieth of its volume of air at atmospheric pressure, 
and that this air will expand in the condenser to a volume inversely 
proportional to the absolute pressure in the condenser. The 
capacity of the air-pump must be sufficient to remove this air 
and the condensed steam and injection-water. 

An air-pump for use with a surface-condenser may be smaller 
than one used with a jet-condenser. In marine work it is com- 
mon to provide a method of changing a surface- into a jet-con- 
denser, and to make the air-pump large enough to give a fair 
vacuum in case such a change should become advisable in an 
emergency. 



DRY-AIR PUMP 



375 



Seaton * states that the efficiency of a vertical single-acting 
air-pump varies from 0.4 to 0.6, and that of a double-acting 
horizontal air-pump from 0.3 to 0.5, depending on the design 
and condition; that is, the volume of air and v^ater actually 
discharged will bear such ratios to the displacement of the 
pump. 

He also gives the following table of ratios of capacity of air- 
pump cylinders to the volume of the engine cylinder or cylinders 
discharging steam into the condenser : 

RATIO OF ENGINE AND AIR-PUMP CYLINDERS. 



Description of Pump. 


Description of Engine. 


Ratio. 


Single-acting vertical .... 


Jet-condensing, 


expansion i^ to 2 


6 to 8 


« <' 


Surface- " 


i^ to 2 


8 to 10 


" " . . . . 


Jet- 


3 to 5 


10 to 12 


" " . . . . 


Surface- " 


3 to 5 


12 to 15 


" " . . . . 


" 


compound . . . 


15 to 18 


Double-acting horizontal . . . 


Jet-condensing, 


expansion i^ to 2 


10 to 13 


<< a 


Surface- " 


" i\ to 2 


13 to 16 


(( i( 


Jet- 


3 to 5 


16 to 19 


« (I 


Surface- " 


3 to 5 


19 to 24 


(t tc 


(( <( 


compound . . . 


24 to 28 



Dry-air Pump. — In the recent development of steam-engineer- 
ing, especially for steam-turbines, great emphasis is given to 
obtaining a high vacuum. For this purpose the old form of air- 
pump which withdraws air and water from the condenser has 
been replaced by a feed-pump which takes water only from the 
condenser, and a dry-air pump which removes the air. The air 
is necessarily saturated with moisture at the temperature in 
the condenser, and allowance must be made for this moisture or 
steam, in the design of the pump. For this purpose Dalton's law 
is used, which says that the total pressure in any receptacle con- 
taining air and vapor is equal to the sum of the pressures due 
to the air and to the vapor. 

* Manual of Marine Engineering. 



376 



COMPRESSED AIR 



If the amount of air brought by the water to a jet-condenser 
can be determined or assumed, a calculation for a dry-air pump 
can readily be made. The leakage to a surface-condenser can- 
not be estimated, and consequently the only way of proportion- 
ing the air-pump for a surface-condenser is that already given 
on page 375. 

To illustrate the method of calculation for a dry-air pump 
use will be made of the data from the test of the Chestnut Hill 
Pumping Station already quoted on page 239. 

The vacuum in the condenser was 27.25 inches of mercury, 
and the barometer stood at 30.25 inches reduced to 32° F., so 
that the absolute pressure was 1.473 of a pound. The con- 
densing water entered the surface-condenser at 5i°.9 F. and left 
at 85°. 2 F.; had there been a jet-condenser this would have been 
the temperature in the condenser and will be used for our 
calculation. Making use of the equation for the quantity of 
condensing water on page 150, we have, 

H - gk _ iii7-i-53-3 _ 
gk - gi 53-3 - 20 

Since the engine used 11.22 pounds of steam per horse-power 
per hour and developed 575.7 horse-power, the total condensing 
water per hour would be 

32 X 11.22 X 575-7 
02,4 

the denominator being the weight of a cubic foot of water. If 
the water brings one-twentieth of its volume of atmospheric 
air, the volume of air will be 166 cubic feet per hour. 

Steam at 85°.2 F. has the pressure of 0.595 ^^ ^ pound abso- 
lute; consequently the pressure 1.473 ^^ ^ pound in the con- 
denser is made up of 0.595 steam-pressure and 0.878 air-pressure. 
The atmospheric pressure is 30.25 inches of mercury or 14.85 
pounds, so that taking account of the influence of the pressures 
and absolute temperatures the volume of air (saturated with 
moisture) to be removed from the condenser per hour is 



CALCULATION FOR AN AIR COMPRESSOR 377 

,66 X ^^"^-^ + ^^'' X '-^^ = 2980 cubic feet. 
459-5 + 51-9 0-878 

Assuming the air-pump to be single-acting and to be con- 
nected directly to the engine which made about 50 revolutions 
per minute, the effective displacement of the air-pump bucket 

should be 

2980 ^ (50- X 60) = 1.0 cubic foot. 

To allow for the effect of the air-pump clearance, imperfection 
of valve-action, and for variation in the temperature of condens- 
ing water, this quantity may be increased by 50 to 100 per cent. 

The engine had 3 J feet for the diameter and 6 feet for the 
stroke of the low-pressure piston, so that its displacement was 
nearly 50 cubic feet; the air-pump had a diameter of 2 feet and 
a stroke of one foot, so that its displacement was 3.14 cubic 
feet; the ratio of displacements was about sixteen. This discrep- 
ancy shows that the conventional method of designing air-pumps 
provides liberal capacity. 

Calculation for an Air Compressor. — Let it be required to find 
the dimensions of an air-compressor to deliver 300 cubic feet of 
air per minute at 100 pounds per square inch by the gauge, and 
also the horse-power required to drive it. 

If it is assumed that the air is forced into the delivery-pipe 
at the temperature of the atmosphere, and, further, that there 
is no loss of pressure between the compressor and the delivery- 
pipe, equation (193) for finding the volume drawn into the 
compressor will be reduced to 

V^ = V^-^ = 300 X — ^ = 2341 cubic feet. 
Pi 14-7 

If now we allow five per cent for imperfect valve-action and 
for heating the air as it is drawn into the compressor the appar- 
ent capacity of the compressor will be 

2341 -^ 0.95 = 2464 cubic feet. 

This is the volume on which the power for the compressor must 
be calculated. 



378 COMPRESSED AIR 

If the clearance of the compressor is 0.02 of the piston dis- 
placement, then the factor for allowing for clearance will be 
1^ i_ 

i-~-^)H = 1 -— ^' ) + — = 0.0332 

m\pj m 100 \ 14.7/ 100 

if the exponent of the equation representing the expansion of 
the air in the clearance is 1.4. Consequently the volume on 
which the dimensions of the compressor must be based is 
2464 ^ 0.9332 = 2640 cubic feet. 

At 80 revolutions per minute the mean piston displacement 
will be 

2640 -^ (2 X 80) = 16.5 cubic feet. 

Assuming a stroke of 3 feet, the mean area of the piston must be 
(144 X 16.5) ^ 3 = 792 square inches. 

Allowing 16 square inches for a piston-rod 4^ inches in diameter 
gives a mean area of 800 square inches for the piston, which 
corresponds very nearly to 32 inches for the diameter of the 
piston. 

The power expended in the compressor-cylinder may be cal- 
culated by equation (190), using for Fj the apparent capacity 

of the compressor, giving 

1.4 — 1 

H.P. = 144 X 14.7 X 2464 X 1-4 I lll^iS '•'' - A= 442. 

33000 X (1.4 — i) (V14.7/ ) 

If the friction of the combined steam-engine and compressor 
is assumed to be 15 per cent the horse-power of the steam- 
cylinder must be 

442 -^ 0.85 = 520. 

If the temperature of the atmosphere drawn into the com- 
pressor is 70° F., then by an equation like (80), page 65, the 

delivery temperature will be 

n-i 1.4-1 



r.-r,(fc)-=(4<.o+,o,(HM)-.,„, 

absolute, or about 493° F. 



CALCULATION FOR AN AIR COMPRESSOR 379 

The calculation has been carried on for a simple compressor, 
but there will be a decided advantage in using a compound com- 
pressor for such work. Such a compressor should have for the 
pressure in the intermediate reservoir 



p' = VP1P2 = v^ii4-7X 14.7 = 41.06 pounds. 

The factor for allowing for clearance of the low-pressure 
cylinder will now be 

x-lg7H-i-=z-^(^Y"^+^ =0.9784. 
m\pj m 100x14.7/ 100 

The loss from imperfect action of the valves and for heating 
of the air as it enters the compressor will be less for a compound 
than for a simple compressor, but we will here retain the value 
2464 cubic feet, previously found for the apparent capacity of 
the compressor. The volume from which the dimensions of the 
compressor will be found will now be 

2464 ^ 0.9784 = 2518 cubic feet, 

which with 80 revolutions per minute will give 15.74 cubic feet 
for the piston displacement, and 755.5 square inches for the 
effective piston area, if the stroke is made 3 feet, as before. 
Adding 16 inches for the piston-rod, which will be assumed to 
pass entirely through the cylinder, will give for the diameter of 
the low-pressure cylinder 31! inches. 

Since the pressure f is a mean proportional between p^ and 
p^y the clearance factor for the high-pressure cylinder will be 
the same as that for the low-pressure cylinder, and, as the volumes 
are inversely proportional to the pressures p^ and f, the high- 
pressure piston displacement will be 

(15.74 X 14.7) -^ 41.06 = 5.64 cubic feet. 

If we allow 8 inches for a rod 4J inches in diameter at one side 
of the piston, then the mean area of the piston will be 278.7 
square inches, which corresponds to a diameter of i8|- inches 
for the high-pressure cylinder. In reality the piston-rod for the 
compound compressor may have a less diameter than the rod for 



380 COMPRESSED AIR 

a simple compressor, because the maximum pressure on both 
pistons will be less than that for the piston of the simple com- 
pressor. Again, the rod which extends from the large to the 
small piston may be reduced in size. But details like these 
which depend on the calculation of strength cannot properly 
receive much attention at this place. 

The power required to drive the compressor may be derived 
from equation (190), replacing v^^, the specific volume, by V^, 
the apparent capacity of the low-pressure cylinder. Using the 
apparent capacity already obtained, 2464 cubic feet, we have 
for the power expended in the air-cylinders 

1.4 — 1 
HP = 2 X 144 X 14-7 X 2464 X 1.4 < / II4-7 Y''''' 1^ = ^77- 
33000 X (1.4 - i) I \i4.7/ ) 

and, as before, allowing 15 per cent for friction of the engine 
and compressor, we have for the indicated horse-power of the 
steam-engine 

377 -^ 0.85 = 444. 

The temperature at the delivery from the low-pressure cylinder 
will be for 70° F. atmospheric temperature 



''(^) 



1.4 — 1 
1.4 

o 



(460 + 70) r—- = 711 



absolute, or 251° F. Since p' is a mean proportional between 
p^ and p^, this will also be the temperature of the air delivered 
by the high-pressure cylinder. 

Friction of Air in Pipes. — The resistance to the flow of a 
liquid through a pipe is represented in works on hydraulics by 
an expression having the form 

f— - (215) 

2g m 

in which ? is an experimental coefficient, u is the velocity in 
feet per second, g is the acceleration due to gravity, I is the 
length of the pipe in feet, and m is the hydraulic mean depth, 



FRICTION OF AIR IN PIPES 381 

which last term is obtained by dividing the area of the pipe 
by its perimeter. For a cylindrical pipe we have consequently 

m = ln(P ^ nd =- Id . . <, . . . (216) 

The expression (215) represents the head of liquid required to 
overcome the resistance of friction in the pipe when the velocity 
of flow is u feet per second. Such an expression cannot properly 
be applied to flow of air through a pipe when there is an appre- 
ciable loss of pressure, for the accompanying increase in volume 
necessitates an increase of velocity, whereas the expression treats 
the velocity as a constant. If, however, we consider the flow 
through an infinitesimal length of pipe, for which the velocity 
may be treated as constant, we may write for the loss of head 
due to friction 

? ........ (217) 

2g m 

This loss of head is the vertical distance through which the air 
must fall to produce the work expended in overcoming friction, 
and the total work thus expended may be found by multiplying 
the loss of head by the weight of air flowing through the pipe. 
It is convenient to deal with one pound of air, so that the expres- 
sion for the loss of head also represents the work expended. 

The air flowing through a long pipe soon attains the tem- 
perature of the pipe and thereafter remains at a constant temper- 
ature, so that our discussion for the resistance of friction may be 
made under the assumption of constant temperature, which 
much simplifies our work, because the intrinsic energy of the air 
remains constant. Again, the work done by the air on enter- 
ing a given length dl will be equal to the work done by the air 
when it leaves that section, because the product of the pressure 
by the volume is constant. 

Since there is a continual increase of volume corresponding 
to the loss of pressure to overcome friction, and consequently 
a continual increase of velocity from the entrance to the exit 
end of the pipe, there is also a continual gain of kinetic energy. 



382 



COMPRESSED AIR 



But the velocity of air in long pipes is small, and the changes of 
kinetic energy can be neglected. 

The air expands by the amount dv as it passes through the 
length dl of pipe, and each pound does the work pdv. This 
work must be supplied by the loss of head, and, since there is 
no other expenditure of energy, the work expended in the loss 
of head is equal to the work done by expansion; consequently 

pdv = ^ (218) 

2g m 

But from the characteristic equation 

pv = RT (219) 



we have 

RT 

P 
which substituted in equation (217) gives 



dv =- — dp, 



^u'dl RT . . , 

^ = — dp .... (220) 

2gm P 

If the area of the pipe is A square feet, and if W pounds of air 
flow through it per second, then 

Wv WRT , , 

u = -—- = — - — (221) 

A Ap ^ ^ 

in which v is the specific volume, for which a value may be 
derived from equation (219). Replacing u in equation (220) 
by the value just derived, we have 

WTR'dl _ _ RT^ 
2gA^p^m p ' 

2gA^m RT 

Integrating between the limits L and o, and p^ and p^, we 
have 

^ gA'm RT ■■■■■■ ^"3; 



FRICTION OF AIR IN PIPES 



383 



But from equation (221) the velocity at the entrance to the pipe 
where the pressure is p^ will be 

WRT , ,,/ ApM, 
^^=__ and W^-l^, 

so that equation (223) may be reduced to 

. A^p,^u,^L _ p,'-p : . 

gA^mR^r RT ' 

" ^gRTm pl ^^^^^ 

Equation (224) may be solved as follows : 
_ ( gRTm p^ 



^- = ^-^^ -- r \ (225) 



\ ^L p, 



^^SRTn^pl-^ ^^^^^ 






The first two forms allow us to calculate either the velocity 
or the loss of pressure; the last form may be used to calculate 
values of ffrom experiments on the flow through pipes. 

From experiments made by Riedler and Gutermuth* Pro- 
fessor Unwin f deduces the following values for ?: 

Diameter of pipe, feet. f 

0.492 0.00435 

0.656 0.00393 

0.980 0.00351 

For pipes over one foot in diameter he recommends for use 

f = 0.003. 

* Neue Erjahrungen uber die Krajtversorgung von Paris durch Drticklujt, 1891. 
t Development and Distribution of Power. 



•i 



384 COMPRESSED AIR 

Replacing the hydraulic mean depth m by id, its value for 
round pipes, and using R = 53.22 and g = 32.16, we have in 
place of equation (226) 

^-47o^r • • • (^^^) 

All of the dimensions are given in feet, but from the form of 
the equation it is evident that the pressures may be in any con- 
venient units, for example, in pounds per square inch absolute. 

For example, let us find the loss of pressure of 300 cubic feet 
per minute if delivered through a six-inch pipe a mile long, the 
initial pressure being 100 pounds by the gauge. 

The velocity of the air w;ll be 

(300 -^ 60) ^ — = 5 -^ -^ = 25.5 feet. 

4 ,4 

The terminal pressure will consequently be 



^ ( ^u.^L ) ( 0.0044 X 25.5 X S28o)^ 

^^ = ^>r-4l^h""-^ r 43°(46o+7o)i 1 

= 107 pounds, 

with 70° F. for the temperature of the atmosphere and with 

? = 0.0044. Consequently the loss of pressure is about eight 

pounds. 

Compressed-air Engines. — Engines for using compressed air 

differ from steam-engines only in details that depend on the 

nature of the working 
fluid. In some instances 
compressed air has been 
used in steam-engines 
without any change; for 
example, in Fig. 84 the 
dotted diagram was taken 
from the cylinder of an 
Fig. 84. engine using compressed 

air, and the dot-and-dash 

diagram was taken from the same end of the cylinder when 




FINAL TEMPERATURE 385 

steam was used in it. The full line ab is a hyperbola, and the 
line ac is the adiabatic line for a gas ; both lines are drawn through 
the intersection of the expans^ion lines of the two diagrams. 

Power of Compressed-air Engines. — The probable mean 
effective pressure attained in the cylinder of a compressed-air 
engine, or to be expected in a projected engine, 
may be found in the same manner as is 
used in designing a steam-engine. In Fig. 
85 the expansion curve i 2 and the com- 
pression curve 3 o may be assumed to be 
adiabatic lines for a gas represented by 
the equation 

and the area of the diagram may be found in the usual way, and 
therefrom the mean effective pressure can be determined. Hav- 
ing the mean effective pressure, the power of a given engine or 
the size required for a given power may be determined directly. 
The method will be illustrated later by an example. 

Air-Consumption. — The air consumed by a given compressed- 
air engine may be calculated from the volume, pressure, and 
temperature at cut-off or release, and the volume, temperature, 
and pressure at compression, in the same way that the indicated 
consumption of a steam-engine is calculated; but in this case 
the indicated and actual consumption should be the same, since 
there is no change of state of the working fluid. Since the 
intrinsic energy of a gas is a function of the temperature only, 
the temperature will not be changed by loss of pressure in the 
valves and passages, and the air at cut-off will be cooler than 
in the supply-pipe, only on account of the chilling action of the 
walls of the cylinder during admission, which action cannot be 
energetic when the air is dry, and probably is not very important 
when the air is saturated. 

Final Temperature. — If the expansion in a compressed-air 
engine is complete, i.e., if it is carried down to the pressure in 
the exhaust-pipe, then, assuming that there are no losses of 



386 COMPRESSED AIR 

pressure in valves and passages, the final temperature may be 
found by the equation 

7-,= nf^M (229) 



^ '-if) 



If the expansion is not complete, then the temperature at the 
end of expansion may be found by the equation 



Tr = T 



m- <-) 



in which Vc is the volume in the cylinder at cut-off and F^ at 
release, Tj. is the absolute temperature at the end of expansion, 
and T3 is the temperature at cut-off, assumed to be the same as 
in the supply-pipe. T^ is not the temperature during back- 
pressure nor in the exhaust- pipe. When the exhaust- valve is 
opened at release the air will expand suddenly, and part of the 
air will be expelled at the expense of the energy in the air remain- 
ing — much as though that air expanded behind a piston, and 
the temperature in the cylinder during exhaust and at the 
beginning of compression may be calculated by equation (229). 
The temperature in the exhaust-pipe will not be so low, for the 
temperature of the escaping air will vary during the expulsion 
produced by sudden expansion, and will only at the end of that 
operation have the temperature T^, while the energy expended 
on that air to give it velocity will be restored when the velocity 
is reduced to that in the exhaust-pipe. 

Volume of the Cylinder. — The determination of the volume 
of the cylinder of a compressed-air engine which uses a stated 
volume of air per minute is the converse of the determination 
of the air consumed by a given engine, and can be found by a 
similar process. We may calculate the volume of air, at the 
pressure in the supply-pipe, consumed per stroke by an engine 
having one unit of volume for its piston displacement, and 
therefrom find the number of units of volume of the piston dis- 
placement for the required engine. 

Interchange of Heat. — The interchanges of heat between 



MOISTURE IN THE CYLINDER 387 

the walls of the cylinder of a compressed-air engine and the air 
working therein are of the same sort as those taking place between 
the steam and the walls of the cylinder of a steam-engine; that 
is to say, the walls absorb heat during admission and compression 
if the latter is carried to a considerable degree, and yield heat 
during expansion and exhaust. Since the walls of the cylinder 
are never so warm as the entering air nor so cold as the air 
exhausted, the walls may absorb heat during the beginning of 
expansion and yield heat during the beginning of compression. 

The amount of interchange of heat is much less in a com- 
pressed-air engine than in a steam-engine. With a moderate 
expansion the interchanges of heat between dry air and the 
walls of the cylinder are insignificant. Moisture in the air 
increases the interchanges in a marked degree, but does not 
make them so large that they need be considered in ordinary 
calculations. 

Moisture in the Cylinder. — The chief disadvantage in the 
use of moist compressed air — and it is fair to assume that 
compressed air is nearly if not quite saturated when it comes 
to the engine — is that the low temperature experienced when 
the range of pressures is considerable causes the moisture to 
freeze in the cylinder and clog the exhaust-valves. The diffi- 
culty may be overcome in part by making the valves and passages 
of large size. Freezing of the moisture may be prevented by 
injecting steam or hot water into the supply-pipe or the cylinder, 
or the air may be heated by passing it through externally heated 
pipes or by some similar device. In the application of com- 
pressed air to driving street-cars the air from the reservoir has 
been passed through hot water, and thereby made to take up 
enough hot moisture to prevent freezing. The study of gas- 
engines suggests a method of heating compressed air which it is 
believed has never been tried. The air supplied to a compressed- 
air engine, or a part of the air, could be caused to pass through 
a lamp of proper construction to give complete combustion, and 
the products of combustion passed to the engine with the air. 
Should such a device be used it would be advisable that the tem- 



388 COMPRESSED AIR 

perature of the air should be raised only to a moderate degree 
to avoid destruction of the lubricants in the cylinder, and the 
combustion at all hazards must be complete, or the cylinder 
would be fouled by unburned carbon. 

Compound Air-Engines. — When air is expanded to a con- 
siderable degree in a compressed-air engine a gain may be 
realized by dividing the expansion into two or more stages in 
as many cylinders, provided that the air can be economically 
reheated between the cylinders. The heat of the atmosphere 
or of water at the same temperature may sometimes be used 
for this purpose. It is not known that machines of this con- 
struction have been used. If they were to be constructed the 
practical advantages of equal distribution of work and pressure 
would probably control the ratio of the volumes of the cylinders. 

Calculation for a Compressed-air Engine. — Let it be required 
to find the dimensions for a compressed-air engine to develop 
100 indicated horse-power at the pressure of 92 pounds by the 
gauge and at 70° F. Assume the clearance to be five per cent 
of the piston displacement, and assume the cut-off to be at 
quarter stroke, the release to be at the end of the stroke, and the 
compression at one-tenth of the stroke. 

If the piston displacement is represented by /), then the volume 
in the cylinder at cut-off will be 0.30 Z), that at release will be 
1.05 Z>, and that at compression will be 0.15 D. The absolute 
pressures during supply and exhaust may be assumed to be 
106.7 ^^d 14.7 pounds per square inch. The work for one 
stroke of the piston will be 



w v^ /: .. r^ , 144X106.7X0.30^^ 
1^=144X106.7X0.252) -{■ -^^ ^^^ 



K — 1 



V1.05/ 



^ 144 X 14-7 X o.i^D i /0.05V'-' ) 

- 144 X 14.7 Xo.oZ) — ^-^ ^^ — ^i— — -] I 

K — 1 ( \o.i5/ ) 

= 144Z) (26.68 + 31.530 - 13.23 - 1.96) = 144 X 43.02D. 

The corresponding mean effective pressure is 43.02 pounds per 
square inch. If the engine is furnished with large ports and 



CALCULATION FOR A COMPRESSED-AIR ENGINE 389 

automatic valve-gear the actual mean effective pressure may 
be 0.9 of that just calculated, or 38.7 pounds per square inch. 

For a piston displacement D the engine will develop at 150 
revolutions per minute 

144 X sS.yP X 2 X ISO , 

• — ^ — horse- power; 

33000 

and conversely to develop 100 horse-power the piston displace- 
ment must be 

^ 100 X 33000 , . . ^ 

D= ^^ = 1.074 cubic feet, 

144 X 38.7 X 2 X 150 

and with a stroke of 2 feet the effective area of the piston will be 

1.974 X 144 -^ 2 = 142. 1 square inches. 

If the piston-rod is 2 inches in diameter it will have an area of 
3.14 square inches, so that the mean area of the piston will be 
143.7 square inches, corresponding to a diameter of 13 J inches. 

We find, consequently, that an engine developing 100 horse- 
power under the given conditions will have a diameter of 13^ 
inches and a stroke of 2 feet, provided that it runs at 150 revo- 
lutions per minute. 

In order to determine the amount of air used by the engine 
we must consider that the air caught at compression is compressed 
to the full admission-pressure of 106.7 pounds absolute. Part 
of this compression is done 'by the piston and part by the entering 
air, but for our present purpose it is immaterial how it is done. 
The volume filled by air at atmospheric pressure when the 
exhaust- valve closes (including clearance) is 0.15 of the piston 
displacement. When the pressure is increased to 106.7 pounds 
the volume will be reduced to 



l2±l) 
\io6.7/ 



of the piston displacement. The volume drawn in from the 
supply-pipe will consequently be 

0.25 +0.05 — 0.017 = 0.283 



390 



COMPRESSED AIR 



of the piston displacement. If the compression occurred suffi- 
ciently early to raise the pressure to that in the supply-pipe 
before the ad mission- valve opened, then only 0.25 of the piston 
displacement would be used per stroke and a saving of about 13 
per cent v^'ould be attained; in such case the mean effective 
pressure would be smaller and the size of the cylinder would be 
larger. 

The air-consumption for the engine appears to be 
2 X 150 X 0.283 X pist. displ. =2X150X0.283X1.974= 167.6 
cubic feet per minute. The actual air-consumption will be 
somewhat less on account of loss of pressure in the valves and 
passages; it may be fair to assume 160 cubic feet per minute for 
the actual consumption. 

In order to make one complete calculation for the use of com- 
pressed air for transmitting power, the data for the compressed- 
air engine have been made to correspond with the results of calcu- 
lations for an air-compressor on page 377 and for the loss of 
pressure in a pipe on page 384. Since there is a loss of pressure 
in flowing through the pipe at constant temperature, there is 
a corresponding increase of volume, so that the pipe delivers 

300 X 114.7 -^ 106.7 = 322.6 
cubic feet per minute. Our calculation for the air-consumption 
of an engine to deliver 100 horse-power gives about 160 cubic 
feet, from which it appears that the system of compressor, con- 
ducting-pipe, and compressed-air engine should deliver 
100 X 322.6 -^ 160 = 200 -f horse-power. 

If the friction of the compressed-air engine is assumed to be 
ten per cent, the power delivered by it to the main shaft (or to 
the machine driven directly from it) will be 

200 X .9 = 180 horse-power. 

The steam-power required to drive a simple compressor was 
found to be 520 horse-power; it consequently appears that 

180 -^ 520 = 0.34 
of the indicated steam-power is actually obtained for doing work 



EFFICIENCY OF COMPRESSED-AIR TRANSMISSION 391 

from the entire system of transmitting power. If, however, a 
compound compressor is used, then the indicated steam-power 
is 444, and of this 

180 -^ 444 = 0.40 
will be obtained for doing work. 

If, however, we consider that the power would in any case be 
developed in a steam-engine, and that the transmission system 
should properly include only the compressor-cylinder, the pipe, 
and the compressed-air engine, then our basis of comparison will 
be the indicated power of the compressor-cylinder. For the 
simple compressor we found the horse-power to be 442, which 
gives for the efl&ciency of transmission 

180 -^ 442 = 0.41, 
while the compound compressor demanded only 3.77 horse- 
power, giving an efficiency of 

180 ^ 377 = 0.48. 

It appeared that the failure to obtain complete compression 
involved a loss of about 13 per cent in the air-consumption. 
It may then be assumed that with complete compression our 
engine could deliver 200 horse-power to the main shaft. In 
that case the efficiency of transmission when a compound com- 
pressor is used may be 0.53. 

Efficiency of Compressed-air Transmission. — The preced- 
ing calculation exhibits the defect of compressed air as a means 
of transmitting power. It is possible that somewhat better 
results may be obtained by a better choice of pressures or pro- 
portions. Professor Unwin estimates that when used on a large 
scale from 0.44 to 0.51 of the indicated steam-power may be 
realized on the main shaft of the compressed-air engine. On 
the other hand, when compressed air is used in small motors, 
and especially in rock-drills and other mining- machinery, much 
less efficiency may be expected. 

Experiments made by M. Graillot * of the Blanzy mines 
showed an efficiency of from 22 to 32 per cent. Experiments 

* Pernolet, L'Air Comprime, pp. 549, 550. 



392 COMPRESSED AIR 

made by Mr. Daniel at Leeds gave an efficiency varying from 
0.255 to 0.455, with pressures varying from 2.75 atmospheres 
to 1.33 atmospheres. An experiment made by Mr. Kraft* gave 
an efficiency of 0.137 for ^ small machine, using air at a pressure 
of five atmospheres vv^ithout expansion. 

Compressed air has been used for transmitting pov^er either 
where pov/er for compression is cheap and abundant, or v^here 
there are reasons why it is specially desirable, as in mining and 
tunnelling. It is now used to a considerable extent for driving 
hand-tools, such as drills, chipping-chisels, and calking-tools, 
in machine- and boiler-shops, and in shipyards. It is also used 
for operating cranes and other machines where power is used 
only at intervals, so that the condensation of steam (when used 
directly) is excessive, and where hydraulic power is liable to give 
trouble from freezing. 

Compressed air has been used to a very considerable extent 
for transmitting power in Paris. The system appears to be 
expensive and to be used mainly on account of its convenience 
for delivering small powers or in places where the cold exhaust 
can be used for refrigeration. The trouble from freezing of 
moisture in the cylinder has been avoided by allowing the air 
to flow through a coil of pipe which is heated externally by a 
charcoal fire. Professor Unwin estimates that an efficiency of 
transmission of 0.75 may be attained under favorable conditions 
when the air is heated near the compressor, but he does not 
include the cost of fuel for reheating in this estimate. 

Storage of Power by Compressed Air. — Reservoirs or cylin- 
ders charged with compressed air have been used to store power 
for driving street-cars. A system developed by Mekarski uses 
air at 350 to 450 pounds per square inch in reservoirs having a 
capacity of 75 cubic feet. The car also carries a tank of hot 
water at a temperature of about 350° F., through which the air 
passes on the way to the motor and by which it is heated and 
charged with steam. This use of hot water gives a secondary 
method of storing power, and also avoids trouble from freezing 

* Revue universelle des Mines, 2 serie, tome vi. 



STORAGE OF POWER BY COMPRESSED AIR 393 

in the motor-cylinders. Air at much higher pressures has been 
used for driving street-cars in New York City, but the particu- 
lars have not been given to the public. 

The calculation for storage of power may be made in much 
the same way as that for the transmission of power; the chief 
difference is due to the fact that the air is reduced in pressure 
by passing it through a reducing-valve on the way from the 
reservoir to the motor. By the theory of perfect gases such 
a reduction of pressure should not cause any change of tem- 
perature, but the experiments of Joule and Thomson (page 69) 
show that there will be an appreciable, though not an important, 
loss of temperature when there is a large reduction of pressure. 
Thus at 70° F. or 2i°.i C. the loss of temperature for each 100 
inches of mercury will be 

o°.92 X /^-^V= o°.79 C. = 11° F. 
\294/ 

Now 100 inches of mercury are equivalent to about 49 pounds 
to the square inch, so that 100 pounds difference of pressure will 
give about 3^° F. reduction of temperature, and 1000 pounds 
difference of pressure will give about 35° F. reduction of tem- 
perature. The last figures are far beyond the limits of the 
experiments, and the results are therefore crude. Again, the air 
in passing through the reducing-valve and the piping beyond 
will gain heat and consequently show a smaller reduction of tem- 
perature. The whole subject of loss of temperature due to 
throttling is uncertain, and need not be considered in practical 
calculations for air-compressors. 

For an example of the calculation for storage of power let us 
find the work required to store air at 450 pounds per square 
inch in a reservoir containing 75 cubic feet. Replacing the 
specific volume v^ in equation (213) by the actual volume, we 
have for the work of compression (not allowing for losses and 
imperfections) 

W^^X 464.7 X 144 X 75 -^:4_j (464:1)'^' _) 

1.4 - I (\ 14.7 / ) 

= 20520000 foot-pounds. 



394 



COMPRESSED AIR 



If the pressure is reduced to 50 pounds by the gauge before it is 
used, the volume of air will be 

75 X 464.7 -^ 64.7 = 539 cubic feet. 
The work for complete expansion of one pound to the pressure 
of the atmosphere will be 

i»'=ft«.+.-^|.-(;^r'i-f.. 



© 



1.4-1 



and the work for 539 cubic feet will be 

1 

144 X 64.7 X 539 ^'^ ^ \ I - {^^ ^ = 5976000 

foot-pounds, without allowing for losses or imperfections. The 
maximum efficiency of storing and restoring energy by the 
use of compressed air in this case is therefore 
5976000 -j- 20520000 = 0.29. 

In practice the efficiency cannot be more than 0.25, if indeed 
it is so high. 

Sudden Compression. — It may not be out of place to call atten- 
tion to a danger that may arise if air at high pressure is suddenly 
let into a pipe which has oil mingled with the air in it or even 
adhering to the side of the pipe. The air in the pipe will be com- 
pressed, and its temperature may become high enough to ignite the 
oil and cause an explosion. That this danger is not imaginary is 
shown by an explosion which occurred under such conditions in 
a pipe which was strong enough to withstand the air-pressure. 

Liquid Air. — The most practical way of liquefying air on a 
large scale is that devised by Linde depending on the reduction 
of the temperature by throttling. On page 69, is given the 
empirical expression deduced by Joule and Kelvin for the 
reduction in temperature of air flowing through a porous plug 
with a difference of pressure measured by 100 inches of mercury, 



0.92 



m 



LIQUID AIR 395 

in which 2 73°. 7 C. is taken to be the absolute temperature of 
freezing, and T is the absolute temperature of the air. 

A modern three-stage air-compressor can readily give a press- 
ure of 2000 pounds per square inch, and if the above expression 
is assumed to hold approximately for such a reduction in pressure, 
it indicates a cooling of 

2000 o ^ 

0.02 X = 37°.S C. 

^ 100 X 0.491 

or about 67° F. By a cumulative effect to be described, the air 
may be cooled progressively till it reaches the boiling-point of its 
liquid and then liquefied. Linde's liquefying apparatus consists 
essentially of an air-compressor, a throttling-orifice, and a heat 
interchange apparatus. 

The air-compressor should be a good three-stage machine 
giving a high pressure. The throttling-orifice may be a small 
hole in a metallic plate. The heat interchange apparatus may 
be made up of a double tube about 400 feet long, the inner tube 
having a diameter of 0.16 and the outer tube a diameter of 0.4 
of an inch ; these tubes for convenience are coiled and are then 
thoroughly insulated from heat. The air from the compressor 
is passed through the inner tube to the throttle-orifice and then 
from the reservoir below the orifice, through the space between 
the inner and outer tubes back to the compressor. The cumu- 
lative effect of this action brings the air to the critical temper- 
ature in a comparatively short period, and then liquid air begins 
to accumulate in the reservoir below the orifice, whence it may be 
drawn off. 

The atmospheric air before it is supplied to the condenser 
should be freed from carbon dioxide and moisture, which would 
interfere with the action, and should be cooled by passing it 
through pipes cooled with water and by a freezing mixture. 
The portion of air liquefied must be made up by drawing air from 
the atmosphere, which is, of course, purified and cooled. 

The principal use of liquid air is the commercial production of 
oxygen by fractional distillation ; several plants have been installed 
for this purpose. 



CHAPTER XVI. 

REFRIGERATING-MACHINES. 

A REFRiGERATiNG-MACHiNE IS a device for producing low 
temperatures or for cooling some substance or space. It may 
be used for making ice or for maintaining a low temperature in 
a cellar or storehouse. 

Refrigeration on a small scale may be obtained by the solu- 
tion of certain salts; a familiar illustration is the solution of 
common salt with ice, another is the solution of sal ammoniac 
in water. Certain refrigerating- machines depend on the rapid 
absorption of some volatile liquid, for example, of ammonia by 
water; if the machine is to work continuously there must be some 
arrangement for redistilling the liquid from the absorbent. The 
most recent and powerful refrigerating- machines are reversed 
heat-engines. They withdraw the working substance (air or 
ammonia) from the cold-room or cooling-coil, compress it, and 
deliver it to a cooler or condenser. Thus they take heat from a 
cold substance, do work and add heat, and finally reject the sum 
of the heat drawn in and the heat equivalent of the work done. 
These reversed heat-engines, however, are very far from being 
reversible engines, not only on account of imperfections and losses 
but because they work on a non-reversible cycle. 

Two forms of refrigerating- machines are in common use, air 
refrigerating- machines and ammonia refrigerating-machines. 
Sometimes sulphur dioxide or some other volatile fluid is used 
instead of ammonia. Carbon dioxide has been used, but there are 
difficulties due to high pressure and the fact that the critical tem- 
perature is 88° F. 

Air Refrigerating-Machine. — The general arrangement of 
an air refrigerating-machine is shown by Fig. 86. It consists 

396 



AIR REFRIGERATING-MACHINE 



397 



of a compression-cylinder A, an expansion-cylinder B of smaller 
size, and a cooler C. It is commonly used to keep the atmos- 
phere in a cold-storage room at a low temperature, and has 
certain advantages for this purpose, especially on shipboard. 
The air from the storage-room comes to the compressor at or 
about freezing-point, is compressed to two or three atmospheres 
and delivered to the cooler, which has the same form as a sur- 
face-condenser, with cooHng water entering at e and leaving at /. 
The diaphragm mn is intended to improve the circulation of 
the cooling water. From the cooler the air, usually somewhat 
warmer than the atmosphere, goes to the expansion-cylinder J5, 




Fig. 86- 

in which it is expanded nearly to the pressure of the air and 
cooled to a low temperature, and then delivered to the storage- 
room. The inlet-valves a, a and the delivery-valves b, b of 
the compressor are moved by the air itself; the ad mission- valves 
Cy c and the exhaust-valves d, d of the expansion-cylinder are 
like those of a steam-engine and must be moved by the machine. 
The difference between the work done on the air in the com- 
pressor and that done by the air in the expansion-cylinder, 
together with the friction work of the whole machine, must be 
supplied by a steam-engine or other motor. ♦ 

It is customary to provide the compression-cylinder with a 
water-jacket to prevent overheating, and frequently a spray 
of water is thrown into the cylinder to reduce the heating and 
the work of compression. Sometimes the cooler C, Fig, 86, 



398 REFRIGERATING MACHINES 

is replaced by an apparatus resembling a steam-engine jet-con- 
denser, in which the air is cooled by a spray of water. In any 
case it is essential that the moisture in the air, as well as the 
water injected, should be efficiently removed before the air is 
delivered .to the expansion-cylinder; otherwise snow will form 
in that cylinder and interfere with the action of the machine. 
Various mechanical devices have been used to collect and remove 
water from the air, but air may be saturated with moisture after 
it has passed such a device. The Bell-Coleman Company use 
a jet-cooler with provision for collecting and withdrawing water, 
and then pass the air through pipes in the cold-room on the 
way to the expansion-cylinder. The cold-room is maintained 
at a temperature a little above freezing-point, so that the mois- 
ture in the air is condensed upon the sides of the pipes and 
drains back into the cooler. 

When an air refrigerating- machine is used as described, the 
pressure in the cold-room is necessarily that of the atmosphere, 
and the size of the machine is large as compared with its per- 
formance. The performance may be increased by running 
the machine on a closed cycle with higher pressures; for example., 
the cold air may be delivered to a coil of pipe in a non-freezing 
salt solution, from which the air abstracts heat through the 
walls of the pipe and then passes to the compressor to be used 
over again. The machine may then be used to produce ice, or 
the brine may be used for cooling spaces or liquids. A machine 
has been used for producing ice on a small scale, without cooling 
water, on the reverse of this principle; that is, atmospheric air 
is first expanded and chilled and delivered to a coil of pipe in 
a salt solution, then the air is drawn from this coil, after absorb- 
ing heat from the brine, compressed to atmospheric pressure, 
and expelled. 

' Proportions of Air Refrigerating-Machines. — The perfor- 
mance of a refrigerating-machine may be stated in terms 
of the number of thermal units withdrawn in a unit of time, 
or in terms of the weight of ice produced. The latent heat of 
fusion of ice may be taken to be 80 calories or 144 b.t.u. 



PROPORTION OF AIR OF REFRIGERATING-MACHINES 399 

Let the pressure at which the air enters the compression- 
cylinder be />p that at which it leaves be p^\ let the pressure at 
cut-ofif in the expanding-cylinder be p^ and that of the back- 
pressure in the same be p^\ let the temperatures correspond- 
ing to these pressures be Z^, t^, /g, and t^, or, reckoned from the 
absolute zero, T^, Tj, Tg, and T^- With proper valve-gear 
and large, short pipes communicating with the cold-chamber 
/)4 may be assumed to be equal to p^ and equal to the pressure 
in that chamber. Also t^ may be assumed to be the tempera- 
ture maintained in the cold-chamber, and /, may be taken to 
be the temperature of the air leaving the cooler. With a good 
cut-off mechanism and large passages p^ may be assumed to 
be nearly the same as that of the air supplied to the expanding- 
cylinder. Owing to the resistance to the passage of the air 
through the cooler and the connecting pipes and passages, p^ 
is considerably less than p^. 

It is essential for best action of the machine that the expan- 
sion and compression of the expanding-cylinder shall be complete. 
The compression may be made complete by setting the exhaust- 
valve so that the compression shall raise the pressure in the 
clearance-space to the admission-pressure p^ at the instant 
when the admission-valve opens. The expansion can be made 
complete only by giving correct proportions to the expanding- 
and compression-cylinders. 

The expansion in the expanding-cylinder may be assumed 
to be adiabatic, so that 

Were the compression also adiabatic the temperature t^ could 
be determined in a similar manner; but the 
air is usually cooled during compression, 
and contains more or less vapor, so that the 
temperature at the end of compression cannot 
Fig. 87. i^Q determined from the pressure alone, even 

though the equation of the compression curve be known. 




400 REFRIGERATING MACHINES 

Let the air passing through the refrigerating- machine per 

minute be M; then the heat withdrawn from the cold-room is 

Q, = Mc, {t, - U) (232) 

The work of compressing M pounds of air from the pressure p^ 
to the pressure p^ in a compressor without clearance is (Fig. 87) 

W^, = M I p,v, + y pdv - p^v^ \ ; 

n - 1 

••• W.= Mp,v^^^\{f-) " -X j . . . . .(.33) 

provided that the compression curve can be represented by an 
exponential equation. If the compression can be assumed to 
be adiabatic, 

K I 

for in such case we have the equations 






^ = (^] ' AR = r,.-c. = c, " 



If the expansion is complete in the expanding-cylinder, as 
should always be the case, then the equation for the work done 
by the air will have the same form as equation (233) or (234), 
replacing /j and p by fi and />4, and t^ and p^ by /, and p^ ; so that 

n — 1 

W'.= KM,;^J(^)"-xj. . .(33s) 
and for adiabatic expansion 

W,= ^(1,-1,) (236) 



PROPORTION OF AIR OF REFRIGERATING-MACHINES 401 

The difference between the works of compression and expan- 
sion is the net work required for producing refrigeration; conse- 
quently 

W=W,-W,= ^U,-h-t,+t4 .(237) 

or, replacing M by its value from equation (232), 

TF = Si ^2 + ^4 - /, - ^3 ^2s8) 

A /j — /4 

The net horse-power required to abstract Q^ thermal units 
per minute is consequently 

33000 i,-h ^ ^^' 

where l^ is the temperature of the air drawn into the compressor, 
and ^2 is the temperature of the air forced by the compressor into 
the cooler, and f^ is the temperature of the air supplied to the 
expanding-cylinder, and U is the temperature of the cold air 
leaving the expanding-cylinder. The gross horse-power devel- 
oped in the steam-engine which drives the refrigerating- machine 
is likely to be half again as much as the net horse-power or even 
larger. The relation of the gross and the net horse-powers for 
any air refrigerating- machine may readily be obtained by indi- 
cating the steam- and air-cylinders, and may serve as a basis for 
calculating other machines. 

The heat carried away by the cooling water is 

Q, = Q,+AW (240) 

If compression and expansion are adiabatic, then 
Q, = Mc^ (/, _ /^ + /^ -f- /, _ /^ _ Q = Mcp {t, - /g) . (241) 

or, replacing M by its value from equation (232), 

Q. = <2. 7^ (242) 

^1 — M 

If the initial and final temperatures of the cooling water are 



402 REFRIGERATING MACHINES 

/, and /*, and if qi and ^^ are the corresponding heats of the 
liquid, then the weight of cooling water per minute is 

G = — 2i_ == Q ^Z_3 . . . (24^) 

The compressor-cylinder must draw in M pounds of air per 
minute at the pressure p^ and, the temperature /j, that is, with 
the specific volume v^\ consequently its apparent piston dis- 
placement without clearance will be at N revolutions per minute, 

Mv, MRT, , , 

2N 2Np^ 

for the characteristic equation gives 

p,v, = RT,. 
Replacing M by its value from equation (232), we have 

Dc = ^^^^\. ' .. .... (245) 

Since all the air delivered by the compressor must pass through 
the expanding-cylinder, its apparent piston displacement will be 

If ^j, the pressure of the air entering the compression-cylinder 
is equal to />4, that of the air leaving the expanding-cylinder (as 
may be nearly true with large and direct pipes for carrying the 
air to and from the cold-room), equation (246), will reduce to 

D. = r),'^ (247) 

Both the compressor- and the expanding-cylinder will have 
a clearance, that of the expanding-cylinder being the larger. 
As is shown on page 363, the piston displacement for an air- 
compressor with a clearance may be obtained by dividing the 
apparent piston displacement by the factor 



m \pj m 



CALCULATION FOR AN AIR-REFRIGERATING MACHINE 403 

If the expansion and compression of the expanding-cylinder are 
complete, the same factor may be applied to it. For a refriger- 
ating-machine n may be replaced by fc for both cylinders. To 
allow for losses of pressure and for imperfect valve action the 
piston displacements for both compressor- and expanding- 
cylinders must be increased by an amount which must be deter- 
mined by practice; five or ten per cent increase in volume will 
probably suffice. In practice the expansion in the expanding- 
cylinder is seldom complete. A little deficiency at this part 
of the diagram will not have a large effect on the capacity of 
the machine, and will prevent the formation of a loop in the 
indicator-diagram; but a large drop at the release of the expand- 
ing-cylinder will diminish both the capacity and the efficiency 
of the machine. 

The temperature t^ and the capacity of the machine may be 
controlled by varying the cut-off of the expanding-cylinder. If 
the cut-off is shortened the pressure p^ will be increased, and 
consequently Ti will be diminished. This will make D^, the 
piston displacement of the expanding-cylinder, smaller. A 
machine should be designed with the proper proportions for its 
full capacity, and then, when running at reduced capacity, the 
expansion in the expanding-cylinder will not be quite complete. 

Calculation for an Air-refrigerating Machine. — Required 
the dimensions and power for an air refrigerating- machine to 
produce an effect equal to the melting of 200 pounds of ice per 
hour. Let the pressure in the cold-chamber be 14.7 pounds per 
square inch and the temperature 32° F. Let the pressure of 
the air delivered by the compressor-cylinder be 39.4 pounds by 
the gauge or 55.1 pounds absolute, and let there be ten pounds 
loss of pressure due to the resistance of the cooler and pipes and 
passages between the compressor- and the expanding-cylinder. 
Let the initial and final temperatures of the cooling water be 
60° F. and 80° F., and let the temperature of the air coming 
from the cooler be 90° F. Let the machine make 60 revolutions 
per minute. 

With adiabatic expansion and compression the temperatures 



404 REFRIGERATING MACHINES 

of the air coming from the compressor- and discharged from the 

expanding-cylinder will be 

qj 

T^ = 492 (^)?= 714; ••• /, = 254° F. 

\I4.// 



T, = (460 + 90) (^ =402; .-. /4= -58° F. 

\44.i/ 

The melting of 200 pounds of ice is equivalent to 

200 X T44 -^ 60 = 480 B.T.u. 

per minute; consequently the net horse-power of the machine 

is by equation (239) 

P^ = 77861 /. + /4 - /. - /. 
33000 t^ - /4 

_ 778 X 480 .. 254 - 58 - 32 - 90 

33000 32+58 

= ^7^ X ^^^ X 74 ^ H. P., 

33000 X 90 

and the indicated power of the steam-engine may be assumed 
to be 14 horse-power. 

By equation (245) the apparent piston displacement of the 
compressor without clearance will be 



2l\Cj,p^ (^ - U) 

2.33 cu. ft. 



2Nc^p, (t, - U) 

480 X .S3. 22 X .102 



2 X 60 X 0.2375 X 144 X 14.7 (32 + 58) 

By equation (247) the apparent piston displacement of the 
expanding-cylinder without clearance will be 

Dg = Dc-;=r = 2.33 X = 1.90 cubic feet. 

^1 492 

If the clearance of the compressor-cylinder is 0.02 of its piston 

displacement, then the factor for clearance by equation (191) is 

i-i(^f+-^---^M'^-^ = o.979, 

m\pj m 100 \i4.7/ 100 



COMPRESSION REFRIGERATING-MACHINES 



405 



SO that the piston displacement becomes 

2.33 -^ 0.979 = 2.38 cubic feet. 
If, further, the clearance of the expander-cylinder is 0.05 of 
its piston displacement, the factor for clearance becomes 



I — 



100 



(-) 



+ 



5 _ 



100 



0.963, 



which makes the piston displacement 

1.90 H- 0.963 = 1.97 cubic feet. 

If now we allow ten per cent for imperfections, we will get for 
the dimensions : stroke 2 feet, diameter of the compressor-cylinder 
15 J inches, and diameter of the expanding-cylinder 14 inches. 

Compression Refrigerating-Machine. — The arrangement of 
a refrigerating- machine using a volatile liquid and its vapor is 




Fig. 



shown by Fig. 88. The essential parts are the compressor A, 
the condenser B, the valve D, and the vaporizer C. The com- 
pressor draws in vapor at a low pressure and temperature, 
compresses it, and delivers it to the condenser, which consists 
of coils of pipe surrounded by cooling water that enters at e and 
leaves at /. The vapor is condensed, and the resulting liquid 



4o6 REFRIGERATING MACHINES 

gathers in a reservoir in the bottom, from whence it is led by a 
small pipe having a regulating-valve D to the vaporizer or 
refrigerator. The refrigerator is also made up of coils of pipe, 
in which the volatile liquid vaporizes. The coils may be used 
directly for cooling spaces, or they may be immersed in a tank 
of brine, which may be used for cooling spaces or for making ice. 
Fig. 88 shows the compressor with one singlcracting vertical 
cylinder which has head-valves, foot-valves, and valves in the 
piston. Small machines usually have one double-acting com- 
pressor cylinder. Large machines have vertical compressors 
which may be single-acting or double acting. 

The cycle which has been stated for the compression 
refrigerating- machine is incomplete, because the working fluid 
is allowed to flow through the expansion-cock into the expanding- 
coils without doing work. To make the cycle complete, there 
should be a small expanding-cylinder in which the liquid could 
do work on the way from the condenser to the vaporizing-coils ; 
but the work gained in such a cylinder would be insignificant, 
and it would lead to complications and difficulties. 

Proportions of Compression Refrigerating-Machines. — The 
liquid condensed in the coils of the condenser flows to the expan- 
sion-cock with the temperature t^ and has in it the heat q^. In 
passing through the expansion-cock there is a partial vaporiza- 
tion, but no heat is gained or lost. The vapor flowing from the 
expansion-coils at the temperature t^ and the pressure p^ is 
usually dry and saturated, or perhaps slightly superheated, as it 
approaches the compressor. Each pound consequently carries 
from the expanding-coils the total heat H^. Consequently 
the heat withdrawn from the expanding-coil by a machine using 
M pounds of fluid per minute is 

Q, = M(H^-q,) (246) 

The compressor-cylinder is always cooled by a water-jacket, 
but it is not probable that such a jacket has much effect on the 
working substance, which enters the cylinder dry and is super- 
heated by compression. We may consequently calculate the 



PROPORTIONS OF COMPRESSION 407 

temperature of the vapor delivered by the compressor by aid of 
equation (80), page 65, giving 

-.'T.(f.y'r.{f.y . . .,.,. 

This equation may be used because it is equivalent to the 
assumption with regard to entropy on page 121. The value 
of a is i for ammonia and 0.22 for sulphur dioxide as given on 
pages 119 and 124. 

As has already been pointed out, the vapor approaching the 
compressor may be treated as though it were dry and saturated, 
each pound having the total heat H^. The vapor discharged by 
the compressor at the temperature /, and the pressure p^ will 

have the heat 

c^ (/, - /J + H^. 

The heat added to each pound of fluid by the compressor is 
consequently 

and an approximate calculation of the horse-power of the com- 
pressor may be made by the equation 

^_ 778M \c,{t, -t,) +H, - HJ 
33000 

or, substituting for M from equation (249), 

^ 778O. ic, (/.-/,) +H,-H,} 

■ 33000 (H,-?,) • • ^'^'> 

The power thus calculated must be multiplied by a factor to 
be found by experiment in order to find the actual power of the 
compressor. Allowance must be made for friction to find the 
indicated power of the steam-engine which drives the motor; for 
this purpose it will be sufficient to add ten or fifteen per cent of 
the power of the compressor. 

The heat in the fluid discharged by compressor is equal to 
the sum of the heat brought from the vaporizing-coils and the 
heat-equivalent of the work of the compressor. The heat that 



(250) 



4o8 REFRIGERATING-MACHINES 

must be carried away by the cooling water per minute is con- 
sequently 

.-, Q, = M\c^{t, -K) ^r,\ (252) 

where r^ is the heat of vaporization at the pressure p^. 

If the cooling water has the initial temperature /„, and the final 
temperature t' ^^ and if qy, and q'y, are the corresponding heats of 
the liquid for water, then the weight of cooling water used per 
minute will be 



M[cJt, 



■^-, ^ (253) 



G = 

qw - q'w 

If the vapor at the beginning of compression can be assumed 
to be dry and saturated, then the volume of the piston displace- 
ment of a compressor without clearance, and making N strokes 
per minute, is 

^ = V • • • • ('54) 

To allow for clearance, the volume thus found may be divided 
by the factor 






<p2 ' ^ 

as is explained on page 363. The volume thus found is further 
to be multiplied by a factor to allow for inaccuracies and 
imperfections. 

The vapors used in compression- machines are liable to be 
mingled with air or moisture, and in such case the performance 
of the machine is impaired. To allow for such action the size 
and power of the machine must be increased in practice above 
those given by calculation. Proper precautions ought to be 
taken to prevent such action from becoming of importance. 

Calculation for a Compression Refrigerating-Machine. — Let 
it be required to find the dimensions and power for an ammonia 
refrigerating- machine to produce 2000 pounds of ice per hour 
from water at 80° F. Let the temperature of the brine in the 



FLUIDS AVAILABLE 409 

freezing-tank be 15° F., and the temperature in the condenser 
be 85° F. Assume that the machine will have one double- 
acting compressor, and that it will make 80 revolutions per 
minute. 

The heat of the liquid for water at 80° F. is 48 b.t.u., and the 
heat of liquefaction of ice is 144, so that the heat which must 
be withdrawn to cool and freeze one pound of water will be 

48 + 144 = 192 B.T.U. 

If we allow 50 per cent loss for radiation, conduction, and 
melting the ice from the freezing-cans, the heat which the machine 
must withdraw for each pound of ice will be about 300 b.t.u.; 
consequently the capacity of the machine will be 

Q^ = 2000 X 300 -7- 60 = loooo B.T.U. per minute. 

The pressures for ammonia corresponding to 15° and 85° F., 
are 42.43 and 165.47 pounds absolute per square inch, so that by 
equation (249) 

r. = r,(fr =(15+460) (i^M7\i^668. 
\pj V 42.43 / 

.-. /, = 668 - 460 = 208° F. 
The horse-power of the compressor is 

P _ 778Q, s^.g--/,) + H, -H,\ 

33000 {H^ - q^) 
^ 778 X loooo jo.50836 (208-85) -f 556 - 535 j _^ 
33000 (535 - 58) 
If we allow 10 per cent for imperfections, the compressor will 
require 45 horse-power. If, further, 15 per cent is allowed for 
friction, the steam-engine must develop 53 horse-power. 

From equation (248) the weight of ammonia used per minute 

is 
M = Q^-r (H^- Q,) = loooo -r (535 - 58) = 21 pounds; 

and by equation (254) the piston displacement for the com- 
pressor will be 

^ Mv^ 21 X 6.03 1 . r . 

D = — — ^ = —^^ = o.gi cubic feet. 

N 2 X 80 ^ 



4IO 



REFRIGERATING-MACHINES 



If lo per cent is allowed for clearance and imperfect valve 
action, the piston displacement will be one cubic foot, and the 
diameter may be made loj inches and the stroke 20 inches. 

Fluids Available. — The fluids that have been used in compres- 
sion refrigeratmg- machines are ether, sulphur dioxide, ammonia, 
and a mixture of sulphur dioxide and carbon dioxide, known as 
Pictet's fluid. The pressures of the vapors of these fluids at sev- 
eral temperatures, and also the pressure of the vapors of methylic 
ether and carbon dioxide, are given in the following table: 



PRESSURES OF VAPORS, MM. OF MERCURY. 



Temperatures 

Degrees 

Centigrade. 


Ether. 


Sulphur 
Dioxide. 

287-5 


Methyl - 
Ether. 


Ammonia. 


Carbon 
Dioxide. 


Pictet's 
Fluid. 


- 30 




576.5 


866.1 




585 


— 20 


68.9 


479-5 


882.0 


1392. I 


15142 


745 


— 10 


114. 7 


762.5 


1306.6 


2144.6 


20340 


1018 





184.4 


1 165. 1 


1879.0 


3183.3 


26907 


1391 


10 


286.8 


1719.6 


2629.0 


4574.0 


34999 


1938 


20 


432.8 


2462 . I 


3586.0 


6387.8 


44717 


2584 


30 


634.8 


3431-8 


4778.0 


8701 .0 


56119 


3382 


40 


907.0 


4670.2 




11595-3 


69184 


4347 



Ether was used in the early compression- machines, but at the 
temperatures maintained in the refrigerator the pressure is 
small and the specific volume large, so that the machines, Hke 
air refrigerating-machines, were either feeble or bulky. More- 
over, air was liable to leak into the machine and unduly heat the 
compressor -cylinder. Sulphur dioxide has been used success- 
fully, but it has the disadvantage that sulphuric acid may be 
formed by the leakage of moisture into the machine, in which 
case rapid corrosion occurs. Ammonia has been extensively 
used in the more recent machines with good results. When 
distilled from an aqueous solution it is liable to contain con- 
siderable moisture. As is shown by the table, Pictet's fluid has 
a pressure at low temperature intermediate between the pressures 
of sulphur dioxide and ammonia, and the pressure increases 
slowly with the temperature. It has been used by the inventor 



ABSORPTION REFRIGERATING APPARATUS 



411 



only, and does not appear in practice to have any advantage over 
ammonia. 

Absorption Refrigerating Apparatus. — Fig. 89 gives an 
ideal diagram of a continuous absorption refrigerating appara- 
tus. It consists of the following essential parts: (i) the gen- 
erator B, containing a concentrated solution of ammonia in 
water, from which the ammonia is driven by heat; (2) the con- 
denser C, consisting of a coil of pipe in a tank, through which 
cold water is circulated; (3) the valve F, for regulating the 
pressures in C and in /; (4) the refrigerator /, consisting of a 
coil of pipe in a tank containing a non-freezing salt solution; 
(5) the absorber A, containing a dilute solution of ammonia, 
in which the vapor of ammonia is absorbed; and (6) the pump 
P for transferring the solution from the bottom of A to the top 
of B\ there is also a pipe connecting the bottom of B with the 
top oi A. It is apparent that the condenser and refrigerator 
or vaporizer correspond to the parts B and C of Fig. 88, and 
that the absorber and generator take the place of the compressor. 
The pipes connecting A and B are arranged to take the most 



B 


c 


1 




1 ' "S 




I 


1 A 




^_ir-^ 





Fig. 89. 



concentrated solution from A to B, and to return the solution 
from which the ammonia has been driven, from B io A. In 
practice the generator B is placed over a furnace, or is heated 
by a coil of steam-pipe, to drive off the ammonia. Also, arrange- 
ments are made for transferring heat from the hot liquid flow- 
ing from B io A io the cold liquid flowing from A to B. As 



412 



REFRIGERATING-MACHINES 



the ammonia is distilled from water in B the vapor driven off 
contains some moisture, w^hich causes an unavoidable loss of 
efficiency. 

Tests of an Air Refrigerating-Machine. — An air refriger- 
ating- machine, constructed under the Bell-Coleman patent, 
was tested by Professor Schroter * at an abattoir in Hamburg, 
where it was used to maintain a low temperature in a storage- 
room. The machine is horizontal, and has the pistons for the 
expansion- and compression-cylinders on one piston-rod, the 
expansion-cylinder being nearer the crank. Power is furnished 
by a steam-engine acting on a crank at the other end of the 
main shaft and at right angles to the crank driving the air- 
pistons. Both the steam-cylinder and the expansion-cylinder 
have distribution slide-valves, with independent cut-off valves. 
The main dimensions are given in the following table: 

DIMENSIONS BELL-COLEMAN MACHINE. 





Steam- 
Cylinder. 


Compression- 
Cylinder. 


Expansion- 
Cylinder. 




Head 
End. 


Crank 
End. 


Head 
End. 


Crank 
End. 


Head 
End. 


Crank 
End. 


Diameter of piston, cm 

Diameter of piston-rod, cm 


53 
8.1 
0.605 
5-9 


53 

0.605 
5.8 


71 
9.0 
605 
1-4 


71 
6.8 
0.605 
1-4 


53 
9.0 
0.605 
8 9 


53 
9.0 
0.605 
8, 


Clearance, per cent of piston displacement . 



Water is sprayed into the compression-cylinder, and the air 
is further cooled by passing through an apparatus resembling 
a steam-engine jet-condenser, after which it is dried by passing 
it through a system of pipes in the cold-room before it passes 
to the expansion-cylinder. 

In the tests, indicators were attached to each end of the several 
cylinders, and the temperature of the air was taken at entrance 
to and exit from each of the air-cylinders. Specimens of the 
indicator-diagrams from the air-cylinders show for the com- 
pressor a slight reduction of pressure during admission and 
some irregularity during expulsion, and for the expansion- 

* Untersuchungen an Kdltemachinen , 188'/. 



TESTS OF AN AIR REFRIGERATING-MACHINE 



413 



cylinder a little wire-drawing at cut-off, and a good expansion 
and compression, though neither is complete. No attempt 
was made to measure the amount and temperatures of the cool- 
ing water. 

The data and results of the tests and the calculations are 
given in Table XXXVI. 

Table XXXVI. 

tests on bell-coleman machine. 



Number of test 

Duration in hours 

Revolutions per minute 

Temperatures of air, degrees Centigrade : 

At entrance to compression-cylinder 

At exit from compression-cylinder . 

At entrance to expansion-cylinder 

At exit from expansion- cylinder 

Mean effective pressure, kgs. per sq. cm.: 

Steam-cj'linder: headend 

crank end 

Compression-cylinder: head end 

crank end 

Expansion -cj'linder: head end 

crank end 

Indicated horse-power : 

Steam-cylinder 

Compression-cylinder 

Expansion- cylinder 

Mean pressure during expulsion from compression-cylinder, kgs. . 
Mean pressure during admission to expansion-cylinder, kgs. . . . 

Difference 

Calculation from compression diagram : 

Absolute pressure at end of stroke, kgs 

Absolute pressure at opening of admission- valve, kg.: 

Head end . 

Crank end 

Volume at admission, per cent of piston displacement : 

Head end 

Crank end 

Weight of air discharged per stroke, kg.: 

Head end 

Crank end 

Weight of air discharged per revolution, kg. . , 

Calculation from expansion diagram : 
Absolute pressure at release, kgs. : 

Head end „ 

Crank end 

Absolute pressure at compression, kgs. : 

Head end 

Crank end 

Volume at release, per cent of piston displacement: 

Head end 

Crank end 

Volume at compression, per cent of piston displacement: 

Head end 

Crank end . 

Air used per stroke, kg. : 

Head end 

Crank end 

Air used per revolution 

Difference of weights, calculated by compression and expansion 

diagrams, kg 

In per cent of the former 

Mean weight of air per revolution, kg 

Elevation of temperature at constant pressure, degrees Centigrade. 
Heat withdrawn per H. P. per hour, calories 



6 
6505 


II. 

1.63 
61.2 


III. 
2.92 
63.5 


193 
27.3 
19.00 
-47.0 


175 

26.8 

16.6 

— 47.0 


19. 1 

27.2 

19. 1 

— 47-0 


2.263 
2.239 

i!869 
1.592 
1. 615 


2.336 
2.294 
I. 861 
1.825 
1.589 
1.594 


2.343 

1.870 
1.906 
1.626 
1.624 


85.12 
128.8s 

60.10 
3-35 
2.82 
0.53 


82.35 
118-55 

56.12 
3-25 
2.83 
0. 42 


85.71 

126.01 

59.46 

0.56 


1.04 


1.04 


1.04 


0.783 
0.765 


0.788 
0.749 


0.764 
0.76s 


6.15 
8.50 


5-95 
8.41 


6.03 
7-91 


0.2744 
0. 2716 
0.546 


0.2764 
0.2742 
0.551 


0.2750 
0.2730 
0.548 


I -32 
I -45 


1-31 

1.44 


1.33 
1.46 


I. 14 
1.20 


1. 14 
1. 19 


1. 17 
1.22 


104.65 
106.1 


104.7 
106.3 


104.8 
106.4 


16.5 
19.8 


16.0 
19.6 


16.6 
20.6 


0.234 
0.254 
0.488 


0.233 
0.254 
0.487 


0.238 

0.2SS 

0.493 


0.058 
10.6 


0.064 
II. 6 


0.05s 
10.0 


0.514 
66.3 
371 


0.519 
64.5 
354 


0.520 

66.1 
363 



Table XXXVII. 

TESTS ON REFRIGERATING MACHINES. 
By Professor Schroter. 



Number. 



I 

2 

3 
4 
5 
6 
7 
8 
o 
19 
II 

12 



6 


Dimensions of the steam 


Dimensions of the 


B 


cylinder. 




compression cylinder. 














■5 




n 




-o\ 


■^1 


6 

£ 












<u c 




i 


tJ o 
.2 a 


Jls 




J-s. 


Hi 


1 


>. 


Q 


Q 


m 


P 


Q 


W 


c^ 














Linde. 


371^25 


55; 5 


800 


32 s 


^3 


540 


;;' 


400 


.... 


602 


250 


55 


420 


'' 


330 


52 


740 


" 


" 


" 


Pictet. 


450 


68 


900 

" 
" 


430 


^5 


900 



36 min. 

34 " 
106 " 

50 " 
46 " 

35 " 

3 hrs. 
3 " 
3.5 " 
11.08" 
9- 83 
4.00 " 



Number. 






"S e 




11 




3 8 

a 


I 


64.8 
59-8 


53-6 
66.1 




2 


45.9 


a 


54-7 
55-1 




26. 27 


4 




27.30 




59- 1 
49.6 
65-15 






6 






7 


26.1 


18. 1 


8 


65.8 
64.2 


34-5 
91.2 


25.8 


9 


52.01 


10 


64.7 


94-5 


61.70 


II 


64.5 


99.2 


66.42 


12 


64.0 




75.02 



Absolute pressures of vapor, 
kilos, per sq. centimeter. 



^ 






1 g 

ill 


1 


2|| 


CI 


C! 


13 










6.99 




9.58 


9.31 

13-66 
14.06 
14. II 
13-78 


2.50 


8.13 


7.87 


2.36 


10.68 


10.41 


2.97 


3-77 


3.22 


0.45 


4. II 


3-50 


0.63 


4- 23 


3.62 


0.73 


5.81 


5-11 


0.67 



Number. 



I 

2 

3 
4 
S 
6 

I 

9 
10 
II 
12 



Ice formed. 






9.0 

8.3 



1.3 
1.3 
1-3 
1-3 






34.8 



16.8 
25.0 
28.2 
20.6 



o V <u 

Uri Cue 
a"" 



15.2 

22.6 
25.9 

18. 5 



2.76 
2.64 

4-851 

4-55) 
4.90) 
4-53) 
4.91 1 
4-55) 
4.27 I 
.4.83I 
2.63 
3.24 
0.82 
1-03 
i-iS 
1.06 



Cooling water. 



aJ 


2 




k 


fc 


6 


K 


4J . 


13 S 


g| 


c 


u. 


II . 19 


22.56 


II. 2 


23.58 


II. 2 


23.04 


II. I 


26. 10 


8.77 


12.41 


8.82 


20.45 


10. IS 


14.0 


10. 1 


15-95 


10.15 


17.20 


10.3 


31 -t 



Temperature of 

water or brine 

cooled. 



-4.4 
-5-9 



—9.50 
—3-1 
—18.2 
— 10. o 
—9.7 
— 6.0s 



-4-4 
-5-9 

2-95 
2.38 



4.71 

-9.97 

-4.1 

-18.2 

-10. o 

-9-7 

-6.0s 



S,K 



■y o o 



4444 
3120 

3249 

3367 

3072 

3263 

3684 
3086 
1674 
2385 
2638 
1958 



TESTS OF COMPRESSION-MACHINES 415 

Tests of Compression-Machines. — In Table XXXVII are given 
the data and results of tests on three refrigerating- machines 
on the Linde system using ammonia, and of a machine on 
Pictet's system using Pictet's fluid, all by Professor Schroter. 
The tests on machines used for making ice were necessarily of 
considerable length, but the tests on machines used for cool- 
ing liquids were of shorter duration. 

The cooling water when measured was gauged on a weir or 
through an orifice. In the tests 3 to 6 on a machine used for 
cooling fresh water the heat withdrawn was determined by 
taking the temperatures of the water cooled, and by gauging 
the flow through an orifice, for which the coefficient of flow was 
determined by direct experiment. The heat withdrawn in 
the tests 7 and 8 was estimated by comparison with the tests 
3 to 6. The net production of ice in the tests i and 2 was deter- 
mined directly; and in the test 2 the loss from melting during 
the removal from the moulds was found by direct experiment 
to be 8.45 per cent. By comparison with this the loss by melting 
in the first test was estimated to be 7.7 per cent. The gross 
production of ice in the refrigerator was calculated from the 
net production by aid of these figures. In the tests 9 to 12 on 
the Pictet machine the gross production was determined from 
the weight of water supplied, and the net production from the 
weight of ice withdrawn. 

A separate experiment on the machine used for cooling brine 
gave the following results for the distribution of power: 

Total horse-power , . 57.1 

Power expended on compressor 19.5 

*' " " centrifugal pump 9.8 

'* '' " water-pump 3.6 

The centrifugal pump was used for circulating the brine 
through a system of pipes used for cooling a cellar of a brew- 
ery. The water-pump supplied cooling water to the condenser 
and for other purposes. 



4i6 



REFRIGERATING-MACHINES 



A similar test on the Pictet machine gave: 

Power of engine alone 7.9 H. P. 

' and intermediate gear 16.6 * ' 

' gear, and pump 20.0 " 



< < (I 



i i i i 



In 1888 comparative tests were made by Professor Schroter, 
on a Linde and on a Pictet refrigerating- machine, in a special 
building provided by the Linde Company which had every 
convenience and facility for exact work. The following table 
gives the principal dimensions of the machines: 



PRINCIPAL DIMENSIONS OF LINDE AND PICTET 
REFRIGERATING-MACHINES. 



Diameter of steam-cylinder, cm 

compressor-cylinder, cm. . . . 

steam piston-rod, cm 

compressor-rod, cm 

Stroke of steam-piston, cm 

compressor, cm 

Diameter of pipe in vaporizers, external, mm 

internal, mm 

Length of pipe in first vaporizer, m 

second vaporizer, m 

Diameter of pipe in condenser, external, mm 

internal, mm. 
Length of pipe in condenser, m 



The Linde machine used ammonia and was allowed to draw 
a mixture of liquid and vapor into the compressor, so that no 
water-jacket was required. The Pictet machine used Pictet 's 
fluid, which is a mixture of sulphur dioxide and carbon dioxide 
and had the compressor cooled by a water-jacket. 

The data and results of the tests are given in Table XXXVIII. 
Five tests were made on each machine. The temperature of 
the salt solution or brine, from which heat was withdrawn by the 
vaporizers, was allowed to vary about three degrees centigrade 
from entrance to exit. The entrance temperatures were intended 




TESTS OF COMPRESSION-MACHINES 



417 



Table XXXVIII. 

TESTS ON REFRIGERATING-MACHINES. 
By Professor M. Schroter, Vergleichende Versuche an Kdltetnaschinen. 



Pictet machine. 



Steam-engine : 

Revolutions per minute 

Indicated horse-power 

Compressor : 

Horse-power 

Mechanical efficiency 

Pressure in condenser, kilograms per square 

centimetre 

Pressure in vaporizer, kilograms per square 

centimetre 

Vaporizer : 

Mean temperature of brine, entrance . . 
Mean temperature of brine, exit .... 

Specific heat per litre 

Initial temperature of brine, entrance . . 

Initial temperature of brine, exit 

Final temperature of brine, entrance . . . 

Final temperature of brine, exit 

Condenser : 

Mean temperature of cooling-water, entrance 
Mean temperature of cooling-water from 

condenser 

Mean temperature of cooling-water from 

jacket 

Initial temperature of condensing-water, 

entrance 

Initial temperature of condensing-water, exit 
Final temperature of condensing-water, 

entrance 

Final temperature of condensing-water, exit 

Error in heat account, per cent 

Refrigerative effect, calories per horse-power 

per hour 



One vaporizer. 



57-0 
21.81 

16.82 
0.771 

3-99 

1-47 

6. 10 
308 
0.850 
6.09 
303 

6. 11 
305 

965 

19 72 

15-5 

9-57 
19.71 

9.67 
19.71 
-t-0.6 

3507 



56.8 



16. 10 
0.771 

391 

1.05 

— 1 .96 
—4.98 

0.847 
— 2.02 

4.99 
— 2.04 
—4.98 

9.60 

19.70 

15-6 

9.64 
19.72 

957 
19.64 
+ 0.6 

2556 



III 



57-1 
18.75 

14.26 
0.761 

3 84 
0.68 

— 9.92 
— 12.91 

0.845 

— 9.91 
— 12.91 

— 9-94 
—12.88 

9.61 

19- 59 

16.8 

9- 58 
1937 

9.61 
19-35 

-Fo.4 

1852 



IV 



57.6 
iS-93 

11.83 
0.743 

425 

0.17 

-17-93 
-20.96 
0.841 
-18.00 
-21.00 
-18.00 



9.68 

19-51 

16.7 

9.68 
19-52 

9.72 
19-59 
-1-3 



59-3 
27.56 

22.91 
0.831 

6.39 

1.05 

— 2.04 
—5.01 

0.846 
—1.99 
—5 02 
—2.05 
—4.96 

9.68 

35-18 

18.6 

9-73 
35 -08 

9.72 
3SOI 
+ 89 

1702 



Linde machine. 



Steam-engine: 

Revolutions per minute 

Horse-power 

Compressor : 

Horse-power 

Mechanical efficiency 

Pressure in condenser, kilograms per .square 
centimetre 

Pressure in vaporizer, kilograms per square 

centimetre 

Vaporizer : 

Mean temperature of brine, entrance . . 

Mean temperature of brine, exit .... 

Specific heat per litre ; . . 

Initial temperature of brine, entrance . . 

Initial temperature of brine, exit 

Final temperature of brine, entrance . . . 

Final temperature of brine, exit 

Condenser : 

Mean temperature of cooling-water, entrance 

Mean temperature of cooling-water, exit 

Initial temperature of water, entrance 

Initial temperature of water, exit . . 

Final temperature of water, entrance 

Final temperature of water, exit . . . 

Error in heat account, per cent . . . 

Refrigerative effect, calories per horse-power 
per hour 



15-53 
0.856 



3-89 

6.00 

2 89 

0.850 

5 98 

2.89 

5-97 

2.94 

9-56 
19.76 

9-56 
19.74 

9-57 
19.74 



4308 



45-1 
18.26 



15-20 
0.833 



-5-02 

0.846 

—2.05 

-5.02 

2.04 

5-04 

9-54 
19.63 

9-SS 
19.42 

9-54 
19-45 
-1.8 

3182 



45-1 
17-03 



[4-31 
0.840 



-9.99 
12.91 

0.843 

■ 9-95 

-12.94 

9-97 

12.89 

9.61 
19.84 

9.61 
19.82 

9.60 
19.89 
- 1.9 

2336 



12.63 
0.805 



1-56 

-17.92 
-20.82 

0.840 
-17.97 
-20.83 
17.96 
20.83 

9.61 
19.72 

9.64 
19.79 

9-56 
19.88 



45-0 
24.41 



21.86 
0.895 



2.95 

-2.03 
- 5-OI 

0.84s 

-2.03 

-5.00 

2.03 

501 

9.68 
35-33 

9.68 
35-45 

9-65 
35-44 
-f I 

2022 



4l8 REFRIGERATING-MACHINES 

to be 6°C., - 2° C, - io° C and - i8° C. The cooling 
water was supplied to the condenser at about 9^.5 C, for all 
tests, and for all but one it left the condenser with a temperature 
of nearly 20° C; the fifth test on each machine was made with 
the exit temperature of the cooling water at about 35° C. 

The pressure in the compressor depended, of course, on the 
temperatures of the brine and the cooling-water. For all the 
tests except the fifth on each machine, the maximum pressure 
of the working substance was nearly constant: about 9 kilograms 
per square centimetre for ammonia and about 4 kilograms for 
Pictet's fluid. The fifth test had considerably higher pressure, 
corresponding to the higher temperature in the condenser. The 
minimum pressure of the working substance of course diminished 
as the brine temperature fell. 

The heat yielded per hour to the ammonia in the vaporizer 
was calculated by multiplying together the amount of brine used 
in an hour, the specific heat of the brine, and its increase of 
temperature. But the initial and final temperatures were not 
quite constant, and so a correction was applied. The heat 
abstracted from the ammonia in the condenser was calculated 
from the water used per hour and its increase of temperature. 
The calculation for Pictet's machine involves also the jacket- 
water and its increase of temperature. A correction is applied 
for the variations of initial and final temperatures of the 
cooling-water. If the heat equivalent of the work of the com- 
pressor is added to the heat yielded by the vaporizer the sum 
should be equal to the heat abstracted by the cooling-water. 
The per cent of difference between these two calculations of 
the heat abstracted by the cooling-water is a measure of the 
accuracy of the tests. 

The refrigerative effect is obtained by dividing the heat yielded 
by the vaporizer by the horse-power of the steam-cylinder. The 
first four tests with constant temperature in the condenser show 
a regular decrease in the refrigerative effect for each machine 
as the temperature of the brine and the minimum pressure of 
the working substance is reduced. The fifth test, with a 



TESTS OF COMPRESSION-MACHINES 



419 



higher temperature in the condenser, shows a less refrigerative 
effect than the second test, which has nearly the same brine 
temperatures. These results are in concordance with the idea 
that a refrigerating- machine is a reversed heat-engine; for a 
heat-engine will have a higher efficiency and will use less heat 
per horse-power when the range of temperatures is increased, 
and per contra, a refrigerating-machine will be able to transfer 
less heat per horse-power as the range of temperatures is 
increased. 

Table XXXIX. 

TESTS ON AMMONIA REFRIGERATING-MACHINE. 
By Professor J. E. Denton, Trans. Am. Soc. Mech. Engr., vol. xii, p. 326. 



Pressure above atrnospliere, pounds per square inch : 

Ammonia from compressor , 

Ammonia back-pressure .' 

Barometer, inches of mercury 

Temperature, degrees Fahrenheit : 

Brine, inlet 

outlet 

Condensing- water inlet 

outlet 

Jacket-water, inlet 

Ammonia-vapor, leaving brine-tank 

entering compressor 

leaving compressor 

calculated 

entering condenser 

Brine, pounds per minute 

Specific gravity 

Specific heat 

Ammonia, lbs. per min. by metre 

from compressor displacement . 
Heat account, b.t.c per minute : 

Given to ammonia by brine 

compressor 

atmosphere 

Total received by ammonia 

Taken from ammonia by condenser 

jackets 

atmosphere 

Total taken from ammonia 

Error, per cent 

Power, etc. : 

Revolutions per minute 

Horse-power steam-cylinder 

compressor 

Mechanical efficiency 

Refrigerative effect: 

Tons of ice (melted) in 24 hours 

B.T.U. abstracted from brine per horse-power minute 
Pounds of ice (melted) per pound of coal 



151 
28 
30.07 

36.76 

28.86 

44-65 

83.66 

44-65 

34-2 

39 

213 

229 

200 

2281 

I -163 

0.82 



14776 

27860 

140 

17702 

17242 

608 

182 

18032 



58.09 
85.0 
65.7 
o.8r 



74-8 

174 

24.1 



II 



152 

8.2 

29-59 

6. 27 
2.03 
56.65 
85-4 
56.7 
14.7 
25 
263 
304 
218 
2173 
1. 174 
0.78 
14.68 



71876 

2320 

147 

9653 

9056 

712 

338 

ioio6 

5 

57-7 
71-7 
54-7 
0.83 

.?6.43 
197 



III 



147 

13 

29.87 

14.29 
2 .29 
46-9 
85.46 
46.9 
3-0 
XO.I3 
239 
260 
209 
942.8 
1. 174 
0.78 
16.67 



8824 
25x8 

167 
1 1 409 
9910 

656 

250 
10816 

3-5 

57.88 
73-6 
59-4 
0.86 

44-64 

197 

17.37 



IV 



161 

.27-5 
30.01 



28.45 
54.00 
82.86 
54-3 
29.2 
34 

221 
237 
168 

2374 

I -174 
0-78 
28-32 
34-51 

14647 

3020 

141 

17708 

17359 
406 
252 

18017 



58.89 
88.6 
71.2 
0.83 

74 56 

196 

23-37 



Table XXXIX gives the data and results of tests made by 
Professor Denton on an ammonia refrigerating-machine. The 



420 REFRIGERATING-MACHINES 

only items requiring explanation are the refrigerative effect 
and the calculated temperature of the vapor leaving the con- 
denser; the latter was calculated bv the equation 

and shows both the cooling effect of the jacket and the error in 
assuming an adiabatic compression. The exponent used here 
is a trifle smaller than that of equation (249) page 407. The 
refrigerative effect was obtained by dividing the b.t.u. given 
to the ammonia in a minute by the horse-power of the steam- 
cylinder. The tons per horse-power in 24 hours was obtained 
by multiplying the refrigerative effect in thermal units per 
minute by the number of minutes in a day and then dividing 
the product by 2000 (the pounds in a short ton) and by 144 
(the heat of melting a pound of ice). The pounds of ice per 
pound of coal was based on an assumed consumption of three 
pounds of coal per horse-power per hour, and was calculated 
by multiplying the b.t.u. per horse-power per minute by 60 
and dividing by 3 X 144. 

The main dimensions of the machine were: 

Diameter of ammonia cylinder (single-acting) 12 inches 

Stroke of ammonia cylinder 30 " 

Diameter of steam-cylinder 18 " 

Stroke of steam-cylinder 36 " 

Diameter of pipe for vaporizer and condenser i " 

Length of pipe in vaporizer 8000 feet 

condenser 5000 " 

Test of an Absorption-machine. — The principal data and 
the results of a test made by Professor J. E. Denton * on an 
absorption ammonia refrigerating- machine are given in Table 
XL. The machine is applied to chill a room of about 400,000 
cubic feet capacity at a pork-packing establishment at New 
Haven, Conn. In connection with this test the specific heat of 
the brine, which served as a carrier of heat from the cold room 
to the ammonia, was determined by direct experiment. The 

* Trans. Am. Soc. Mech. Eng., vol. x, May, 1889. 



TEST OF AN ABSORPTION-MACHINE 



421 



Table XL. 

TEST OF AN ABSORPTION-MACHINE. 
Seven Days' Continuous Test, Sept. 11-18, 18 



. f Generator 

Average pressures j „ 

above atmosphere "j p , 

in lbs. per sq. in. (^ Absorber ! 



Average tempera- 
tures in Fahren- 
heit degrees. 



Atmosphere in vicinity of machine . . . . 

Generator 

^ . (Inlet 

^""^ (Outlet 

Condenser I ^"^^f^^- [[[[[[[]][ 

Inlet 

(Outlet 

r Upper outlet to generator . . . . 
Heater-^ Lovi^er " " absorber , . . . 

Linlet from absorber 

Inlet from generator 

Water returned to main boilers from steam 
coil . .• 



Absorber 



Average range off Condenser 
temperature s"! Absorber . 
Fahr. degrees. I Brine . . 



Brine circulated per ( Cubic feet 
hour. i Pounds . 



Specific heat of brine 

Cooling capacity of machine in tons of ice per day of 24 hours 
Steam consumption per hour, to volatilize ammonia, and to 
ojjerate ammonia pump pounds 



British thermal 
units: 



Eliminated Pe^ P°^"d^«^ b""^ • ' ' ' 
( Total per hour 

Of refrigerating effect per pound of steam 

consumption 

^ . . J ( At condenser, per hour .... 

^ ^ I At absorber " .... 

fOn entering generator 

Per pound of steamy ^ , .■■'■■' 
On leaving generator 

I coil 

Consumed by generator per lb. of steam 

condensed 



Condensing water per hour, in pounds 

Equivalent ice production per pound of coal, if one pound of coal 

evaporates ten pounds of steam at boiler 

Calories, refrigerating effect per kilogram of steam consumed . . 
Approximate c o i 1 r Condensing coil 

surface in sq. ft. < Absorber " 

( Steam " 



150-77 
47.70 
23.69 

23-4 

80 

272 

21 .2 

16.16 

54i 

80 

80 
III 
212 
178 
132 
272 

260 

25i 

5 13 

1.633-7 
119,260 

0.800 
40.67 

1,986 

4.1 
481,260 

243 

918,000 

1,116,000 

1,203 

271 

932 
36,000 

17. 1 

135 

870 

350 
200 



422 REFRIGERATING-MACHINES 

brine chilled and the cooling water used were measured with 
meters, which were afterwards tested under the conditions of 
the experiment. 

It is interesting to compare the refrigerative effects expressed in 
pounds of ice per pound of coal. On this basis the compression- 
machine tested by Professor Denton has an advantage of 

24.1 -17. 1 ^, 

' — X 100 = 10 per cent. 

24.1 

But this comparison is really- unfair to the compression- 
machine, for its steam-engine is assumed to require a consump- 
tion of three pounds of coal per horse-power per hour, while the 
calculation for the absorption-machine is based on the assumption 
that a pound of coal can evaporate ten pounds of water; but an 
automatic condensing-engine of the given power should be able 
to run on 20 or 22 pounds of steam per horse-power per hour. 



CHAPTER XVIL 

FLOW OP^ FLUIDS. 

Thus far the working substance has been assumed to be at 
rest or else its velocity has been considered to be so small that 
its kinetic energy has been neglected; now we are to consider 
thermodynamic operations involving high velocities, so that the 
kinetic energy becomes one of the important elements of the 
problem. These operations are clearly irreversible and conse- 
quently the first law of thermodynamics only is available, and if 
any element of computation involves reference to equations that 
were deduced by aid of the second law, care must be taken 
that such computations are allowable. It is true that all prac- 
tical thermal operations are irreversible for one reason or another; 
for example, the cycle for a steam engine is irreversible, both 
because steam is supplied and exhausted from the cylinder and 
because the cylinder is made of conducting material. But all 
adiabatic operations in cylinders (which serve as the basis of 
theoretical discussions) are properly treated as reversible and all 
the deductions from the second law may be applied to that part 
of the cycle. In particular the limitations of the discussion of 
entropy on page 32 have been observed. 

Three cases of continuous thermal operations have been 
discussed (i) flow through a porous plug, (2) the throttling 
calorimeter, (3) friction of air in pipes; to which it may be well 
to return now. In all, the velocity of the fluid has been so small 
that its kinetic energy was neglected; in none of them was any 
reference made to equations deduced by the aid of the second 
law of thermodynamics. Rather curiously, all the operations 
were adiabatic, using the word to mean that no heat was taken 
from or lost to external objects; in the case of transmission of air 
in pipes, this comes from the natural conditions of the case 

423 



424 FLOW OF FLUIDS 

and in the other two operations there was careful insulation 
from heat. None of the operations are isoentropic; for instance, 
the entropy of steam supplied to the calorimeter on page 192 
is about 1.60 and the entropy of the superheated steam in the 
calorimeter is about 1.72; but this does not enter into the solution 
of the problem and is more curious than useful. 

The flow of fluids through orifices and nozzles has become 
even of more importance than formerly on account of the develop- 
ment of steam turbines. Thus far all computations have been 
based on adiabatic action, and when attempt is made to allow 
for friction it is done by the application of an experimental 
factor to results from adiabatic computations. 

The following is the customary method of establishing the 
fundamental equation. Suppose that a fluid is flowing from 

the larger pipe A into the pipe B; 
u , there will clearly be an increase in 

l2— — p— velocity, with a reduction in pressure, 
f The first law of thermodynamics 



Fig. 90 as expressed by equation (16), page 14, 

needs the addition of a term to take 

account of the change in kinetic energy, and may be written 

dQ = A {dE + dW + dK); 

the last term in the parenthesis represents the increase of kinetic 

energy. 

Let it be supposed that there is a frictionless piston in each 

cylinder; the piston in A exerts the pressure p^ on the fluid in 

front of it, and the piston in B has on it the fluid pressure p^. 

Each unit of weight of fluid passing from A through the orifice 

has the work p^v^ done on it, while each pound entering the 

cylinder B does the work p^v^. The assumption of pistons is 

merely a matter of convenience, and if they are suppressed the 

same conditions with regard to external work will hold. 

If the velocity in A is V^ the kinetic energy of one unit of 

72 y 2 

weight in that cylinder is — ^ ; the kinetic energy in B is — ^ 

2g 2g 

for a velocity V^. 



TEST OF AN ABSORPTION-MACHINE 425 

The intrinsic energies in A and B are E^ and E^. If there 
is no heat communicated to or from the fluid the sum of the 
intrinsic energy, external work, and kinetic energy must remain 
constant, so that 

this is the fundamental equation for the flow of a fluid. 

If the walls of the pipes are well insulated there will not be 
much radiation or other external loss even if the pipes have 
considerable length, and in cases that arise in practice that loss 
may properly be neglected. There is likely to be a considerable 
frictional action even if the pipes are short, and the logical method 
appears to call for the introduction of frictional terms at this 
place. Such is not the custom, and a substitute will be dis- 
cussed later. 

Usually the velocity in the large cylinder A is small and the 
term depending on it may be neglected. Solving for the term 
depending on the velocity in B and dropping the subscript, 
we have 

^ = £,-£, + p,v^ - p,v.^ .... (256) 

Incompressible . Fluids. — There is little if any change of 
volume or of intrinsic energy in a liquid in passing through an 
orifice under pressure, so that the equation of flow becomes in 
this case 

V' 

— = (/^l - P2>1 ' (257) 

If the difference of pressure is due to a dift'erence of level or 
head, hy we have 

Pi — P2 ^ ^^' 

where d is the density, or weight of a unit of volume, and is the 
reciprocal of the specific volume; consequently equation (257) 
reduces to 

— = ^, (258) 

2^ 



426 FLOW OF FLUIDS 

which is the usual equation for the flow of a liquid through a 
small orifice. 

Flow of Gases. — The intrinsic energy of a unit of weight of 
a gas is 

pv 



E = 



fc — I 



which depends only on the condition of the gas and not on any 
changes that have taken or may take place. The equation for 
the flow of a gas therefore becomes 

At this place it is customary to use the equation 

/'zV = Pi'^i" (259) 

for the reduction of the equation (258) just as though we were 
dealing with an adiabatic expansion in a non-conducting closed 
cylinder. Now the fact that the isoenergic line and the iso- 
thermal line are practically identical (page 63) shows that a 
perfect gas has no disgregation energy and consequently for an 
adiabatic change all the change in intrinsic energy is available 
for doing outside work, which in this case is applied to increasing 
the kinetic energy of the gas, instead of being applied to the 
piston of a compressed air motor. If this analogy is allowed 
equation (258) may be used, and will yield 

K I 

P2V2 = Z-.^. (^J~'= P'^'^ipj ' • ■ ■ (260) 

so that equation (259) may be reduced to 



YL 

2g 



='.%-^[--(ff'] • ■ • ■<^-' 




FLOW OF GASES 427 

This equation may also be deduced for the 
work of air in the cylinder of a compressed 
^ air motor (Fig. 91). The work of admission 
is p^v^\ the work of expansion is by equation 
F»°- 9- (81), page 65. 

&i--eri=s[--g;n 

and the work of exhaust is 

K T 

so that the effective work is 

which is readily reduced to equation (261). 

For the calculation of velocities it is convenient to replace the 
coefficient p^v^ in equation (261) by RT^, since pressures and 
temperatures are readily determined and are usually given, thus 

n.^r,-^r.-(fcpl . .(.6.) 

2g '/C - I L \pj J 

If the area of the orifice is a, then the volume discharged per 
second is 

aV, 

and the weight discharged per second is 

aV 

w = — , 

when v^ is the specific volume at the lower pressure and is equal 
to 



428 FLOW OF FLUIDS 

Substituting V from equation (262) and v^ from (263) and 
reducing 

The equations deduced for the flow of air apply to the flow 
from a large cylinder or reservoir into a small straight tube 
through a rounded orifice. The lower pressure is the pressure 
in the small tube and differs materially from the pressure of the 
space into which the tube may deliver. In order that the flow 
shall not be much affected by friction against the sides of the 
tube it should be short — not more than once or twice its diameter. 
The flow does not appear to be affected by making the tube 
very short, and the degree of rounding is not important; the 
equations for the flow of both air and steam may be applied 
with a fair degree of approximation to orifices in thin plates and 
to irregular orifices. 

Professor Fliegner * made a large number of experiments on the 
flow of air from a reservoir into the atmosphere, with pressures 
in the reservoir varying from 808 mm. of mercury to 3366 mm. 
He used two different orifices, one 4.085 and the other 7.314 mm. 
in diameter, both well rounded at the entrance. 

He found that the pressure in the orifice, taken by means of 
a small side orifice, was 0.5767 of the absolute pressure in the 
reservoir so long as that pressure was more than twice the atmos- 
pheric pressure; under such conditions the pressure in the orifice 
is independent of the pressure of the atmosphere. 

. If the ratio -^ is replaced by the number 0.5767 and if k, is 

replaced by its value 1.405 in equation (264) we shall have for 
the equation foi the flow of a gas 

7£; = 0.4822a y^-^ (265) 

* Der Civilingenieur, vol. xx, p. 14, 1874. 



FLIEGNER'S EQUATIONS FOR FLOW OF AIR 429 

For the flow into the atmosphere from a reservoir having a 
pressure less than twice the atmospheric pressure Fliegner found 
the empirical equation 



.■ = o.9644Vf- \/-^— ^' • • • 



(266) 



where p^ is the pressure of the atmosphere. 

These equations were found to be justified by a comparison 
with experiments on the flow of air, made by Fliegner himself, 
by Zeuner, and by Weisbach. 

Although these equations were deduced from experiments 
made on the flow of air into the atmosphere, it is probable that 
they may be used for the flow of air from one reservoir into 
another reservoir having a pressure differing from the pressure 
of the atmosphere. 

Fliegner's Equations for Flow of Air. — Introducing the 
values for g and R in the equations deduced by Fliegner, we have 
the following equations for the French and English systems of 
units : 

French units. 

p^ > 2p„ w = o.sgsa-^; 



p,<2p,„ u>^ 0.790a v/ ^- ^\ ^"K 

-* 1 



English units. 
P. 



Pi > 2p„, W = 0.530a 



Vr, ' 



P, < 2P,, W = 1. 060a V^ ^' ^ ^"^ 

p^ = pressure in reservoir; 
pj = pressure of atmosphere; 

T'j = absolute temperature of air in reservoir (degrees centi- 
grade, French units; degrees Fahrenheit, English units). 



430 



FLOW OF FLUIDS 



In the English system p^ and pa are pounds per square inch, 
and a is the area of the orifice in square inches, while w is the 
flow of air through the orifice in pounds per second. If desired, 
the area may be given in square feet and the pressures in pounds 
on the square foot, as is the common convention in thermo- 
dynamics. 

In the French system w is the flow in kilograms per second. 
The pressures may be given in kilograms per square metre 
and the area a in square metres; or the area may be given in 
square centimetres, and the pressures in kilograms on the same 
unit of area. If the pressures are in millimetres of mercury, 
multiply by 13.5959; ^^ ^^ atmospheres, multiply by 10333. 

Theoretical Maxima. — From a discussion of the mean velocity 
of molecules of a gas Fliegner deduces for the maximum velocity 
through an orifice 



V max = '^gRT^ = 16.9 Vr, 

in metric units. His ratio of pressure 0.5767 inserted in equation 
(262) gives 

V max = 17. 1 Vrj. 

The algebraic maximum of equation (264) occurs for the 
ratio p2 -^ Pi = 0-5274, but this figure probably has no physical 
significance. 

Flow of Saturated Vapor. — For a mixture of a liquid and its 
vapor equation (no), page 95, gives 

£=-(? + ^f ), 

so that equation (256) gives for the adiabatic flow from a recep 
tacle in which the initial velocity is zero 

— =7 (?1 - ?2 + ^iPl - ^2^2) + Pl'^l ~ P2'^2' (267) 
2g /t 

Substituting for v^ and v^ from 

V = xu -\- 0-, 



i 



FLOW OF SATURATED VAPOR 43 1 

But 

p + Apti = r; 

.-. A —= x/j - x^r^ + ?i - ?2 + ^^ (Pi - p2)- (268) 
2^ 

The last term of the right-hand member is small, and fre- 
quently can be omitted, in which case the right-hand member is 
the same as the expression for the work done per pound of steam 
in a non-conducting engine, equation (143), page 136, except 
that as in that place the steam is assumed to be initially dry, x^ 
is then ynity. The intrinsic energy depends only on the con- 
dition of the steam, and consequently reference to the second 
law of thermodynamics first comes into this discussion with 
the proposal to compute the quality x^ in the orifice by aid of 
the standard equation for entropy 






2' 



the acceptance of this method infers that the flow of steam 
through a nozzle differs from its action in the cylinder of an 
engine in that the work done is applied to increasing the kinetic 
energy of the steam instead of driving the piston. 

Values of the right-hand member of equation (268) may be 
found in the temperature-entropy table which was computed 
for solving problems of this nature. 

The weight of fluid that will pass through an orifice having 

an area of a square metres or square feet may be calculated by 

the formula 

aV 
w = "-— (268). 

The equations deduced are applicable to all possible mixtures 
of liquid and vapor, including dry saturated steam and hot 
water. In the first place steam will be condensed in the tube, 
and in the second water will be evaporated. 



432 FLOW OF FLUIDS 

If Steam blows out of an orifice into the air, or into a large 
receptacle, and comes to rest, the energy of motion will be turned 
into heat and will superheat the steam. Steam blowing into the 
air will be wet near the orifice, superheated at a little distance, 
and if the air is cool will show as a cloud of mist further from the 
orifice. 

Rankine's Equations. — After an investigation of the experi- 
ments made by Mr. R. D. Napier on the flow of steam, Rankine 
concluded that the pressure in the orifice is never less than the 
pressure which gives the maximum weight of discharge, and 
that the discharge in pounds per second may be calculated by 
the following empirical equations: 

p, = or > - pa, w = a^; 
3 70 

3 42 ( 2p, ) 

in which p^ is the pressure in the reservoir, p^ is the pressure of 
the atmosphere, both in pounds on the square inch, and a is the 
area in square inches. 

The error of these equations is liable to be about two per cent; 
but the flow through a given orifice may be known more closely 
if tests are made on it at or near the pressure during the flow, 
and a special constant is found for that orifice. 

Grashoff's Formula. — For pressures exceeding five-thirds 
of the external or back pressure Grashoff gives the following 
formula for the discharge of steam through a converging orifice, 

w = 15.26 ap^-^"^ 

the weight being in grams per second, the area in square centi- 
metres and the pressure in kilograms per square centimetre. 
For English units the equation becomes 

w = 0.0165 ap^'^'' 

the discharge being in pounds per second, the area in square 
inches and the pressure in pounds absolute per square inch. 
Rateau shows that this formula is well verified by his experiments 



FLOW OF SUPERHEATED STEAM 



433 



on the flow of steam, and that when the pressure is less than 
that required by the formula the flow can be represented by a 
curve which has for coordinates the ratio of the back pressure 
to the internal pressure and for ordinates the ratio of the actual 
discharge to that computed by the equation on the preceding page. 
The following values were taken from his curves: 



Ratio of back pressure 
to internal pressure. 


Ratio of actual to computed discharge. 


Converging orifice. 


Orifice in thin plates. 


0-95 


■ 0.45 


0.30 


0.90 


0.62 


0.42 


0.85 


0-73 


0.51 


0.80 


0.82 


0.58 


0-75 


0.89 


0.64 


0.70 


0.94 


0.69 


0.65 


0.97 


0-73 


0.60 


0.99 


0.77 


0.55 




0.80 


0.45 




0.82 


0.40 




0.83 



He further gives a curve for the discharge from a sharp-edged 
orifice from which the third column was taken. 

Flow of Superheated Steam. — Though there is no convenient 
expression for the intrinsic energy of superheated steam, and 
though the general equation (256) cannot be used directly, an 
equation for velocity can be obtained by the addition of a term 
to equation (268) to allow for the heat required to superheat 
one pound of steam, making it read 



2g Jt, 



cdt + r^ + q^- xj,^ - q^. 



(269) 



The accompanying equation for finding the quality of steam x^ is 

'^ cdt r^ 
T T. 






+ e. 



^2^2 



+ ^, 



(270) 



Here / and T are the thermometric and the absolute temper- 
atures of the superheated steam, t^ is the temperature of saturated 
steam at the initial pressure, and t^ the temperature at the final 



434 



FLOW OF FLUIDS 



pressure, and the letters r^ and r^ and 0^ and 0^ represent the 
corresponding heats of vaporization and entropies of the liquid. 

Both equations apply only if the steam becomes moist at the 
lower pressure, which is the usual case. They may obviously 
be modified to apply to steam that remains superheated, but 
such a form does not appear to have practical application. 

The method of reduction of the integrals in equation (269) 
and (270) is given on page 114; attention is called to the fact 
that the temperature-entropy table affords ready solution of 
equation (269), also of the velocity flow during which the steam 
remains superheated. 

Flow in Tubes and Nozzles. — The velocity of air or steam 
flowing through a tube or nozzle with a large difference in pressure 
is very high, reaching 3000 feet a second in some cases; and 
consequently the effect of friction is marked even in short tubes 
and nozzles. A test by Buchner * on a straight tube 3.52 inches 
long and 0.158 of an inch internal diameter, under an absolute 
pressure of 177 pounds to the square inch delivered only about 
0.9 of the amount of steam calculated by the adiabatic method, 
and the pressure in the tube fell gradually from 131 pounds near 
the entrance to 14.5 pounds near the exit when delivering to a 
condenser at about atmospheric pressure. If there were any 
use for such a device in engineering the problem would appear 
to call for a method of dealing with friction resembling that on 
page 380 for flow of air in long pipes, but probably more difficulty 
would be found in getting a satisfactory treatment. 

From the investigations that have been made on the flow of 
steam through nozzles it appears that they should have a well- 
rounded entrance, the radius of the curve of the section at entrance 
being half to three-fourths of the diameter of the smallest 
section or throat; from the throat the nozzles should expand 
gradually to the exit, avoiding any rapid change of velocity, 
as such a change is likely to roughen the surface where it occurs. 
The longitudinal section may well be a straight line joined to 
the entrance section by a curve of long radius. The taper of 

*MeiUeil ungen uber Forsehungrarheit Heft, i8, p. 43. 



FRICTION HEAD 



435 



the cone may be one in ten or twelve; this will give for the total 
angle at the apex of the cone 5° to 6°; if the entrance to the nozzle 
is not well rounded there will be a notable acceleration of the 
steam approaching the nozzle and this acceleration outside of 
the nozzle appears to diminish the amount of steam that the 
nozzle can deliver. The expansion should preferably be suffi- 
cient to reduce the steam to the pressure into which the nozzle 
delivers; otherwise the acceleration of the steam will continue 
beyond the nozzle, but the steam tends more and more to mingle 
with the adjacent fluid through which it moves, and a poorer 
effect is likely to be obtained. 

If the expansion in the nozzle is not enough to reduce the 
pressure of the steam to (or nearly to) the external pressure into 
which the nozzle delivers, sound waves will be produced and 
there will be irregular action, loss of energy, and a distressing 
noise. On the other hand if the expansion in the nozzle reduces 
the pressure of the steam below the external pressure at the 
exit, sound waves will be set up in the nozzle with added resist- 
ance. This latter condition is likely to be worse than the 
former, and if the pressures between which the nozzle acts 
cannot be controlled it should be so designed as to expand 
the steam to a pressure a little higher than that against which 
it is expected to deliver, allowing a little acceleration to occur 
beyond the nozzle. 

Friction Head. — In dealing with a resistance to the flow of 
water through a pipe, such as is caused by a bend or a valve, 
it is customary to assume that the resistance is proportional to 
the square of the velocity and to modify equation (258), page 
425 to read 

h = h C — J 

where C is a factor to be obtained experimentally. The term 
containing this factor is sometimes called the head due to the 
resistance or required to overcome the resistance, and the 
equation may be changed to 



436 FLOW OF FLUIDS 

it being understood that of the available head h, a certain portion 
h' is used up in overcoming resistances and the remainder is 
used in producing the velocity V. This aspect is well expressed 
by shifting h^ to the other side of the equation and writing 



1/2 

~ = h - h' ^ h 



(.-f) = M.-,). 



This method has been used by writers on steam turbines to 
allow for frictional and other resistance and losses. It must 
be admitted that it is a rough and unsatisfactory method, but 
perhaps it will serve. The value of y probably varies between 
0.05 and 0.15 for flow through a single nozzle or set of guide 
blades or moving buckets in a steam turbine. 

There is one difference between the behavior of water and 
an elastic fluid like air or steam that must be clearly understood, 
and kept in mind. Frictional resistance and other resistances 
to the flow of water, transform energy into heat and that heat 
is lost, or if it is kept by the water is not available afterwards 
for producing velocity; on the other hand the energy which 
is expended in overcoming frictional or other resistances of 
like nature by steam or air, is changed into heat and remains in 
the fluid, and may be available for succeeding operations. 

Experiments on Flow of Steam. — There are five ways of 
experimenting on the flow of steam through orifices and nozzles 
that have been applied to test the theory of flow. Some of them, 
used separately or in combination, can be made to give values 
of the friction factor y, 

(i) Steam flowing through an orifice or a nozzle may be 
condensed and weighed. 

(2) The pressure at one or several points in a nozzle may 
be measured by side orifices or by a searching-tube; the latter 
may be used to investigate the pressure in the region of the 
approach to the entrance, or in the region beyond the exit, and 
may also be used with an orifice. 



BUCHNER'S EXPERIMENTS 437 

(3) The reaction of steam escaping from a nozzle or an orifice 
may be measured. 

(4) The jet of steam may be allowed to impinge on a plate 
or curved surface and the impulse may be measured. 

(5) A Pitot tube may be introduced into the jet and the 
pressure in the tube can be measured. 

Of course two or more of the methods may be used at the same 
time with the greater advantage. It will be noted that none of 
the methods alone or in combination can be made to determine 
the velocity of the steam, and that all determinations of velocity 
equally depend on inference from calculations based on the 
experiments. 

Formerly the weight of steam discharged was considered of 
the greatest importance, as in the design of safety-valves, or in 
the determination of the amount of steam used by auxiliary 
machines during an engine-test. The first method of experi- 
menting was obviously the most ready method of determining 
this matter, and was first applied by Napier in 1869, and on his 
results were based Rankine's equations. 

Since the development of steam turbines much importance is 
given to determination of steam velocities, though it is probable 
that the determination of areas is still the more important 
method, as on it depends the distribution of work and pressure, 
while a considerable deviation from the best velocity will have 
an unimportant influence on turbine efficiency. The first 
experiments on reaction were by Mr. George Wilson in 1872, 
but as his tests did not include the determination of the weight 
discharged they are less valuable. 

Biichner's Experiments. — A number of experimenters have 
determined the weight of steam discharged by nozzles and tubes 
and at the same time measured the pressure in side-orifices at 
one or more places. The most complete appear to be those of 
Dr. Karl Biichner * on the flow through tubes and nozzles. 
Omitting the tests on tubes and on nozzles with a very small 

* Mitteilungen uber Forschungsarbeiten Heft 18, p. 47. 



438 



FLOW OF FLUIDS 



taper, the nozzles for which results will be quoted have the fol- 
lowing designations and dimensions: 



NOZZLES TESTED BY DR. BUCHNER, 

INCHES. 



ALL DIMENSIONS IN 















Distance 


Designa- 


Total 


Cylindri- 


Conical 


Diameter 


Taper 


first side 
orifice 
from 


tion. 


length. 


cal part. 


part. 


at throat. 


one m. 














entrance. 


2a 


1.97 


0.36 


1.61 


0.158 


20 


0-33 


2b 


1.97 


0.36 


I. 61 


0.158 


13 


0-33 


3a 


0-945 


0.37 


I 365 


0159 


7.2 


0-34 


3b 


0-945 


0-37 


1-365 


0.159 


4-9 


0.34 


5c 


1-37 


0-37 


I .00 


0.200 


20.3 


0.24 


5d 


1-37 


0-37 


1. 00 


0.200 


14.2 


0.24 



Distance 

last side 

orifice 

from exit . 



0.17 
0.17 
0.14 
0.14 
O.II 
O.II 



All the nozzles had a cylindrical portion for which the length 
is given in the above table including the rounding at entrance. 
Excluding the rounding, this cylindrical portion was two or three 
times the diameter at the throat and appears to have had consid- 
erable influence on the distribution of the pressure. There were 
from one to three additional side orifices evenly distributed; 
from pressure in these orifices Biichner makes interesting com- 
putations concerning the behavior of the fluid in the tube, but 
the results are not different from those that are brought out by 
the investigations of Stodola and are not included in this dis- 
cussion. The data and results from such of the tests as appear 
to bear on our present purpose of investigating the discharge and 
friction of nozzles are given on page 439. 

Steam for these tests was taken from a boiler through a sepa- 
rator which probably delivered steam with a fraction of a per cent 
of priming. The pressures were all measured on one gauge by 
aid of an eight-way-cock. The steam from the nozzles was con- 
densed and weighed; the experimenter estimates the error due 
to uncertainty of draining the condenser at two per cent, which 
appears to be the maximum error to be attributed to any, of the 



BUCHNER'S EXPERIMENTS 



439 



results. The discharge was also computed by Grashofif's 
equation on page 432, and the ratio to the actual discharge is 
that set down in the table; the variation from unity is not greater 
than the probable maximum error. The method of the compu- 
tation of velocities at throat and exit by the experimenter is not 
very clear, but it was made to depend on the equation (268), using 
the proper pressure and the discharge computed by Grashoff's 
equation. 



TESTS ON FLOW OF STEAM. 
Dr. Karl Buchner. 



Number 
and 


Pressure pounds absolute. 


Ratio of 
throat to 
initial. 


Dis- 
charge 
pounds 
per 


Ratio 
of actual 
to com- 
puted 
dis- 
charge. 


Velocity 
at throat 


Velocity 
at exit. 


Ratio 
of actual 


designa- 










puted 




Initial 


Throat. 


Exit. 


External 




second. 






velocity. 


i-2a 


182 


104.4 


25-3 


13-6 


0-573 


. 0503 




i8co 


3030 


0.928 


2-2 a 


160.5 


94.4 


21.7 


13-6 


0-577 


0.0449 


ir.^ 


1790 


3020 


0.930 


3-2a 


147-3 


83.0 


20.7 


13-8 


0.564 


0.041 I 





1820 


2990 


0.926 


4-2a 


131-3 


75-1 


i«-5 




0.572 


0.0370 




1790 


2990 


0.929 


5-2a 


117. 1 


67.6 


16.8 


13.8 


0.577 


0.0331 




1780 


2960 


0.925 


33-2b 


180.2 


92.1 


16.5 


14. 1 


0.511 


0.0494 




I94t) 


3260 


0.920 


2>^2>^ 


149-9 


76.8 


21.2 


13-6 


0.529 


0.0394 


"^ 


i860 


3060 


0.957 


37-3a 


131-5 


70.4 


19-5 


13-8 


0-535 


0.0363 


0^ +-• 


1850 


3020 


0.950 


3«-3a 


II5-7 


62.0 


17-4 


13-8 


0536 


0.0219 





1850 


3020 


0.944 


39-3 b 


183.6 


99.6 


18.5 


18.5 


0.541 


0.0501 




1830 


3430 


0.987 


41-5 1> 


103.0 


68.6 


38.1 


15-4 


0.660 


. 0483 




1550 


2190 


0.932 


42-5b 


89-3 


58.7 


32.8 


14.9 


0.658 


0.0419 


00 f< 

^0 g 


1550 


2180 


0.932 


43-5^ 


75-2 


49-3 


27-9 


14.7 


0.656 


0.0343 


1560 


2150 


0.923 


44-5 b 


61.0 


37-6 


22.3 


14-5 


0.643 


0.0282 


'-' 


1560 


2160 


0.929 


45-5 b 


45-4 


23. 


16.9 


14-5 


0.618 


0.021 1 




1630 


2130 


0.923 


47-5C 


102.5 


65-4 


25-9 


I5-0 


0.637 


0.0549 




1630 


2520 


0.927 


48-5C 


88.8 


55-7 


22.2 


14.8 


0635 


0.0410 


r^ M 


1630 


2530 


0.931 


49-5C 


74.2 


46.9 


18.5 


14.6 


0-633 


0.0344 


s 


1620 


2530 


0.935 


50-5C 


59-2 


37-1 


14.9 


14.4 


0.625 


0.0277 


M ^ 


1630 


2490 


0.932 



The nozzles 3a and 36 had tapers of i 7.2 and i .'4.9 which were 
probably too great, so that they may not have been filled with 



440 FLOW OF FLUIDS 

Steam; this might account for the small ratio of the throat to the 
initial pressure; the nozzle 26, which had a taper of 1:13, also 
shows a small ratio of throat to initial pressure. 

The most interesting feature of the tests is the ratio of the 
^•elocity at exit, computed by the method referred to above, from 
the pressure at the side orifice near the exit from the nozzle. This 
does not appear to depend on the throat pressure. Leaving 
out tests on the nozzles 3a and 3^ the mean value of this ratio is 
about 0.93 which corresponds to a value y = 0.14. 

Rateau's Experiments. — These tests * have already been 
referred to in connection with Grashoff's formula. They differ 
from most tests oh the discharge from orifices and nozzles in 
that the steam was condensed by a stream of cold water which 
formed a jet condenser; the amount of steam was computed 
from the rise of temperature and the amount of cold water used, 
which latter was determined by flowing it through an orifice. 
He estimates his error at something less than one per cent. The 
number of tests is too large to quote here; it may be enough to 
say that his diagrams show a very great regularity in his results, 
so that whatever error there may be is to be attributed to the 
method, which does avoid, as he claims, the uncertainty of 
draining a condenser. 

Kneass' Experiments. — In order to determine the pressure 
in steam-nozzles such as are used in injectors, Mr. Strickland L. 
Kneass | made investigations with a searching-tube, having a 
small side orifice, both when the nozzles were performing their 
usual function in an injector and when discharging freely into 
the atmosphere. He also used side orifices bored through the 
nozzles for the same purpose. The most interesting feature of 
his investigation is that it makes practically no difference whether 
the discharge is free or into the combining tube of an injector. 

* Experimental Researches on Flow of Steam, trans. H. B. Brydon. 
t Practice and Theory of the Injector. J. Wiley & Sons, 1894. 



ROSENHAIN'S EXPERIMENTS ^^I 

For a well-rounded nozzle such as is used for an injector having 
a taper of one to six, he found the following results : 



Absolute Pressure. 




Calculated Veloc- 


litial. Throat. 


Ratio. 


ity at Throat. 


135 82.0 


0.606 


1407 


105 61.5 


0-585 


1448 


75 42 


0-559 


149 1 


45 24.5 


0.546 


1504 



Stodola's Experiments. — In his work on Steam Turbines, 
Professor Stodola gives the results of tests made by himself on the 
flow of steam through a nozzle, having the following proportions : 
diameter at throat 0.494, diameter at exit 1.45, and length from 
throat to exit 6.07, all in inches. The nozzle had the form of a 
straight cone with a small rounding at the entrance; the taper was 
1 16.37. Four side orifices and also a searching-tube were used to 
measure the pressure at intervals along the nozzle; the searching- 
tube was a brass tube 0.2 of an inch external diameter closed at 
the end and with a small side orifice. This orifice was properly 
bored at right angles; two other tubes with orifices inclined, 
one 45° against the stream and one 45° down stream, gave results 
that were too large and two small by about equal amounts. 

Stodola made calculations with three assumptions (i) with no 
frictional action, (2) with ten per cent for the value oiy, and (3) 
with twenty per cent ; comparing curves obtained in this way for 
the distribution of pressures with those formed by experiments, 
he concludes that the value of y for this nozzle was fifteen per cent. 

Rosenhain's Experiments. — The most recent and notable 
experiments on flow of steam with measurement of reactions 
were made at Cambridge by Mr. Walter Rosenhain.* Steam 
was brought from a boiler through a vertical piece of cycle- 
tubing to a chamber which carried the orifices and nozzles at its 
side; the reaction was counteracted by a wire that was attached 
to the chamber passed over an antifriction pulley to a scale 
pan, to which the proper weight could be added. Afterwards 
he determined the discharge by collecting and weighing steam 

* Proc. Inst. Civ. Eng., vol. cxl, p. 199. 



442 



FLOW OF FLUIDS 



under similar conditions. The steam pressure was controlled by 
a throttle-valve. It is probable that there was some moisture in 
the steam at high pressured and that at low pressures the steam 
was slightly superheated. The following table gives the dimen- 
sions of the nozzles: 

ROSENHAIN'S EXPERIMENTS DIMENSIONS. 



Designation. 


Least Diameter. 


Greatest Diameter. 


Taper. 


I 


0.1873 




. 


II 


0.1840 


0.287 


I : 20 


IIA 


0.1866 






IIB 


0.1849 


0.287 


I : 20 


III 


0.1882 


0.368 


I : 12 


IIIA 


0.1882 


0.255 


I : 12 


IIIB 


0.1882 


0.241 


I : 12 


IV 


0.1830 


0255 


I :3o 


IVA 


0.1830 


. 2.42 


I 130 


IVB 


0.1830 


0.230 


I : 30 


IVC 


0.1830 


0.217 


I :3o 


IVD 


0.1830 


0.205 


I 130 



I was an orifice with sharp edge; IIA had a sharp edge at entrances; the 
several orifices numbered III and IV had slightly rounded entrances. 

DATA AND RESULTS. 











Velocities. 






N-zzle. 


Ratio of 


Proper initial 








Coefficient 


diameter. 


pressure. 








of friction. 








Adiabatic 


Expt. 


Ratio. 




II 


1.56 


150 


2900 


2740 


0.946 


0.105 


III 




96 


275 


3280 








IIIA 




36 


97i 


2600 


2530 


0.972 


0.045 


IIIB 




28 


80 


2460 


2220 


0.903 


0.185 


IV 




39 


^05 


2630 


2400 


0.913 


0.166 


IVA 




32 


90 


2520 


2340 


0.929 


0.137 


IVB 




26 


77i 


2440 


2200 


0.901 


0.188 


IVC 




19 


62i 


2220 


2030 


0.914 


0.165 


IVD 




12 


SO 


2100 


1920 


0.914 


0.165 



A calculation has been made by the adiabatic method to 
determine the pressures for which the several nozzles tested 
would expand the steam down to the pressure of the atmosphere; 



PRESSURE IN THE THROAT ^^^ 

a direct calculation cannot be made, but a curve can readily be 
determined from which the pressure can be interpolated. The 
velocities corresponding to these pressures have been taken from 
Rosenhain's curves and the velocities were calculated also by the 
adiabatic method. Since the diagrams in the Proceedings are to 
a small scale the deduction of pressures from them cannot be very 
satisfactory, but the results are probably not far wrong. The 
table on page 442 gives the coefficient of friction obtained by 
this method. 

Lewicki's Experiments. — These experiments were made by 
allowing the jet of steam to impinge on a plate at right angles 
to the stream, and measuring the force required to hold the plate 
in place; from this impulse the velocity may be determined. 
It was found necessary to determine by trial the distance at 
which the greatest effort was produced. One of his nozzles had 
for the least diameter 0.237 and for the greatest diameter 0.305 
of an inch or a ratio of 1.28, which is proper for a pressure of 80 
pounds per square inch absolute. His experiments gave the 
following results as presented by Biichner: 

Steam pressure 77 99 108 

Ratio of computed and } a a 

expt. velocities i * * 

Coefficient of friction .... 0.08 0.08 0.09 
These experiments like those for reaction are liable to be vitiated 
by expansion and acceleration of the steam beyond the orifice. 

Pressure in the Throat. — Some of the tests by Biichner show 
rather a low pressure in the throat of the nozzle, but in general 
tests on the flow of steam show a pressure in the throat about 
equal to 0.58 of the initial pressure provided that the back pres- 
sure has less than ratio 3/5 to the initial pressure; this corresponds 
with Fliegner's results and should be expected from his com- 
parison with molecular velocity on page 430. The following 
table gives results of tests made by Mr. W. H. Kunhardt * in 
the laboratories of the Massachusetts Institute of Technology: 
The excess of the throat pressure above 0.58 of the initial 

* Transactions Am. Soc. Mech. Engs., vol. xi, p. 187. 



444 



FLOW OF FLUIDS 



pressure for the tests numbered i to 9 is to be attributed to the 
excessive length of the tube. Longer tubes tested by Biichner, 
showed the same efifect in an exaggerated degree. 

FLOW OF STEAM THROUGH SHORT TUBES WITH ROUNDED 

ENTRANCES. 
Diameters 0.25 of an inch. 









Pressure above at- 




Ratio of 






Flow in pounds 
per hour. 










mosphere, pounds 




absolute 


^ 












per square inch. 




pressures. 











i 

JS 
M 
g 


1 








k 

11 




1 

s . 

II 

u 


c 
.2 3 

is 
S1^ 




k 




1 
1 

> 


u 

JQ 

9 

V 




II 

ill 


J 

'2 V: . 

m 




If 

<u u 


It 

fn 


1.5 


3 

8" 
1 

If 

1- 




hJ 


Q 


< 


M 


<"" 


cq 


(^ 


ci; 


H 


PM 


n 





u 


tj 


I 


1.5 


30 


74.1 


14.8 


41.2 


14.7 


0.332 


0.630 


126.2 


1.2 


221.0 


217.0 


224 


1.018 


2 




30 


71.0 


13.2 


39.6 


14.8 


0.326 


0.634 


138.7 


1.5 


213.0 


207.8 


215 


1.025 


3 


" 


20 


72.6 


19.7 


40.6 


14.7 


0.394 


0.634 


141.4 


0.5 


216.0 


211. 4 


220 


1.022 


4 


" 


20 


75.9 


20.4 


42.6 


14.7 


0.387 


0.632 


139.8 


0.7 


228.0 


219.3 


227 


1.040 
1. 016 


5 


" 


20 


71.9 


24-5 


40.6 


14.7 


0.454 


0.638 


140.6 


0.7 


2I3-0 


209.7 


218 


6 


Oj5 


30 


72.8 


14.8 


39.0 


14.8 


0.338 


0.614 


138.7 


0.3 


225.0 


213.6 


221 


1.053 
1.056 
1,046 


7 




20 


72.1 


20.4 


38.8 


14.8 


0.405 


0.617 


142.2 


0.5 


223.5 


211.7 


219 


8 


" 


30 


72.6 


24.7 


39.0 


14.8 


0.452 


0.616 


144.0 


0.5 


223.0 


213.1 


220 


C' 


" 


30 


73-1 


29.9 


39-2 


14.8 


0.509 


0.61S 


145.2 


0.5 


225.5 


213.0 


222 


1.054 
1.054 


10 


0.2 s 


30 


72.6 


24.8 


36.1 


14.9 


0.454 


0.583 


143.8 


0.4 


225,0 


213.5 


220 


II 




30 


72.6 


19.9 


36.1 


14.9 


0.398 


0.583 


141.6 


0.4 


225.0 


213.5 


220 


1.054 
1.066 
1.058 
1.060 


12 


<( 


30 


72.7 


14.9 


36.2 


14.8 


339 


0.583 


140. 5 


0.4 


227.0 


213.0 


220 


13 


" 


30 


126.3 


27.8 


69.0 


14.7 


0.295 


0.594 


155.C 


0.5 


358.8 


338.9 


355 


14 




30 


125.0 


40.8 


67.9 


14.7 


0.398 


0.59? 


157.C 


0.2 


355.0 


334-8 


352 



Design of a Nozzle. — Required the dimensions of a nozzle 
to deliver 500 pounds of steam per hour with a steam pressure of 
150 pounds by the gauge and a vacuum of 26 inches of mercury. 
The vacuum of 26 inches can be taken as substantially equiva- 
lent to 2 pounds absolute and the steam pressure may be taken 
as 165 pounds absolute. The throat pressure is then nearly 
96 pounds absolute. Assuming the steam to be initially dry, 
the calculation can be arranged as follov^^s: 

x,r,= T, (^+ 0^-e\ =784.1 (1.0367 +0.5235 -0.4704) =855.1 

'V3 = ^3(j-+^i -^3) =585.8(i.o367+o.5235-o.i756)=8io.8 

1', + q, - x,v^ - ^2 = 855.9 + 337-7 - 855-1 - 295-1 = 43-4 
^1 + 9i - ^3*^3 - ?3 = 855-9 + 337-7 - 810.8 - 94.3 = 288.5. 



DESIGN OF A NOZZLE 445 

The quantities just obtained are the amounts of heat that 
would be available for producing velocity if the action were 
adiabatic. In order to find the probable velocity allowing for 
friction, they should be multiplied by 1 — y, where y the coeffi- 
cient for friction may be taken as 0.15 for the determination of 
the exit velocity F3. As for the throat velocity, there are two 
considerations, the frictional effect is small because the throat is 
near the entrance, and all experiments indicate that orifices and 
nozzles which are not ' unduly long deliver the full amount of 
steam that the adiabatic theory indicates; therefore we may 
make the calculation for that part of the nozzle by the adiabatic 
method. The available heats for producing velocity may there- 
fore be taken as 

43.4 and (i - 0.15) 288.5 = 245, 
and the velocities are therefore (see page 436) 



v^ = V64.4 X 778 X 43.4 = 1480. 



F3 = V64.4 X 778 X 245 = 3500. 

The quahty of steam in the throat is 

^2 = ^■^2 ^ ^2 = 855-1 - 885.9 = 0-967- 

To find the quality of steam at the exit we may consider that 
if x^' is the actual quality allowing for the effect of friction we 
have 

^ + ?i - ^>3 - ?3 = 245 

^z = (855-9 + 337-7 - 245 - 94.3) ^ 1026 = 0.833. 

Though not necessary for the solution of the problem it is 
interesting to notice that adiabatic expansion to the exit pressure 
would give for 

^3 "" ^3^3 "^ ^3 == 810.8 ^ 1026 = 0.790. 

Now 500 pounds of steam an hour gives 

— 2 
500 -^ 60 = 0.139 



446 FLOW OF FLUIDS 

of a pound per second; consequently the areas at the throat and 
the exit will be by equation (268), page 431, in square inches 

x,u^ +0- 
144^2 = 144 X 0.139 



2""2 



= 144 X 0.139 (0'9^7 ^ 4-55^ + 0.016) -T-1480 = 0.0597; 
14403 = 144 X 0.139 i'^'^33 X 173-6 + 0.016) ^ 3500 = 0.827. 
The diameters are, therefore, 

^2 = 0.280 ^^3 = 1.026. 

If the taper is taken to be one in ten, the conical part will have 
a length of 

10 (1.026 — 0.280) = 7.46 inches; 

and allowing for the rounding at the entrance and for a fair curve 
joining the throat to the cone, the total length may be eight 
inches. 

A nozzle to expand steam to the pressure of the atmosphere 
only, would have the computation for the exit made as follows : 

•^3^3= T^\f + ^i -6'3J = 67i.5(i.o37o+o.5235-o.3i25)=838.o; 

^ + ?i - ^3^3 - ?3 = 855-9 + 337-7 - 838.0 - 180.3 = 175.3. 
Taking the coefficient for friction as o.io the available heat 
appears to be 158.0 and the velocity at exit will be 

F3 = \/64.4 X 778 X 158 = 2810. 
The quality of the steam comes from the equation 
^1 + ?i - <^3 - ?3 = 158.0. 
•'. < = (855-9 + 337-7 - 158 - 180.3) -^ 965.8 = 0.885. 
The area at the exit will now become 
144^3 = 144 X .139 (0.885 X 26.64 + 0.016) -H 2810 = 0.168, 

and the corresponding diameter is 0.462 of an inch. Taking 

the taper as one in ten, the length of the conical part of the nozzle 

becomes 

10 (0.462 — 0.283) = 1.79 inches, 

and its total length including throat and inlet may be 2.3 inches. 



CHAPTER XVIII. 

INJECTORS. 

An injector is an instrument by means of which a jet of steam 
acting on a stream of water with which it mingles, and by which 
it is condensed, can impart to the resultant jet of water a sufficient 
velocity to overcome a pressure that may be equal to or greater 
than the initial pressure of the steam. Thus, stearrf from a 
boiler may force feed-water into the same boiler, or into a boiler 
having a higher pressure. The mechanical energy of the jet of 
water is derived from the heat energy yielded by the condensation 
of the steam-jet. There is no reason why an injector cannot be 
made to work with any volatile liquid and its vapor, if occasion 
may arise for doing so; but in practice it is used only for forcing 
water. An essential feature in the action of an injector is the 
condensation of the steam by the water forced; other instruments 
using jets without condensation, like the water-ejector in which 
a small stream at high velocity forces a large stream with a low 
velocity, differ essentially from the steam-injector. 

Method of Working. — A very simple form of injector is shown 
by Fig. 91, consisting of three essential parts; a, the steam-nozzle^ 
bf the combining-tube, and c, the delivery -tube. Steam is supplied 
to the injector through a pipe connected at d\ water is supplied 
through a pipe at/, and the injector forces water out through the 
pipe at e. The steam-pipe must have on it a valve for startjng 
and regulating the injector, and the delivery-pipe leading to the 
boiler must have on it a check-valve to prevent water from the 
boiler from flowing back through the injector when it is not 
working. The water-supply pipe commonly has a valve for 
regulating the flow of water into the injector. 

This injector, known as a non-lifting injector, has the water- 
reservoir set high enough so that water will flow into the injector 

447 



448 



INJECTORS 



through the influence of gravity. A lifting injector has a special 
device for making a vacuum to draw water from a reservoir 
below the injector, which will be described later. 

To start the injector shown by Fig. 91, the steam- valve is first 
opened slightly to blow out any water that may have gathered 
above the valve, through the overflow, since it is essential to have 
dry steam for starting. The steam-valve is then closed, and 
the water- valve is opened wide. As soon as water appears at the 
overflow between the combining-tube and the delivery-tube the 



w<.sssss\w 




Fig. 91. 



Steam- valve is opened wide, and the jet of steam from the steam- 
nozzle mingles with and is condensed by the water and imparts 
to it a high velocity, so that it passes across the overflow space 
between the combining-tube and the delivery-tube and passes 
into the boiler. When the injector is working a vacuum is liable 
to be formed at the space between the combining and delivery- 
tubes, and the valve at the overflow closes and excludes air 
which would mingle with the water and might interfere with 
the action of the injector. 

Theory of the Injector. — The two fundamental equations of 
the theory of the injector are deduced from the principles of the 
conservation of energy and the conservation of momenta. 



THEORY OF THE INJECTOR 449 

The heat energy in one pound of steam at the absolute pressure 
p^ in the steam-pipe is 

where r^ and q^ are the heat of vaporization and heat of the liquid 

corresponding to the pressure p-^\- is the mechanical equivalent 

/\. 

of heat (778 foot-pounds), and x^ is the quality of the steam; if 
there is two per cent of moisture in the steam, then x^ is 0.98. 

Suppose that the water entering the injector has the tempera- 
ture /g, and that its velocity where it mingles with the steam is F/ ; 
then its heat energy per pound is 



and its kinetic energy is 



2^ 
where q^ is the heat of the liquid at t^, and g is the acceleration 
due to gravity (32.2 feet). 

If the water forced by the injector has the temperature ^4, and 
if the velocity of the water in the smallest section of the delivery- 
tube is Vy„ then the heat energy per pound is 



j?« 



and the kinetic energy is 



V 2 

Let each pound of steam draw into the injector y pounds of 
water; then, since the steam is condensed and forced through 
the delivery-tube with the water, there will be i + >' pounds 
delivered for each pound of steam. Equating the sum of the 
heat and kinetic energies of the entering steam and water to the 
sum of the energies in the water forced from the injector, we 
have 

^ (V. + ?.) + Ki ?3 + ^)Mi + ,) (^ ,. + ^) (.69) 



450 INJECTORS 

The terms depending on the velocities VJ and F„ are never 
large and can commonly be neglected. 

To get an idea of the influence of the former, v^e may consider 
that the pressure forcing water into a non-lifting injector is sel- 
dom, if ever, greater than the pressure of the atmosphere, and 
the corresponding pressure for a lifting injector is always less. 
Now, the pressure of the atmosphere is equivalent to a head of 

/?/ = 144 X 14.7 -r- 62.4 = 34 feet. 

A liberal estimate of y (the pounds of water per pound of 
steam) is fifteen. Therefore, 

y '2 

y _^^ = yl^f _ j^ X 34 = 510. 

In order that an injector shall deliver water against the steam- 
pressure in a boiler its velocity must be greater than would be 
impressed on cold water by a head equivalent to the boiler- 
pressure. Taking the boiler- pressure at 250 pounds by the 
gauge, or 265 pounds absolute, the equivalent head will be 

h = 144 X 265 -^ 62.4 = 610 feet. 

Again taking fifteen for y^ the value of the term depending on Vy, 
will be 

V ^ 
(i + y) — ^ = (i + 15) 610 = 9150. 
2^ 

But the steam supplied to an injector is nearly dry and at 
265 pounds absolute 

^ + 9i = 826.2 + 379.6 = 1205.8, 
so that the term depending on that quantity will have the value 
778 X 1206 = 939000. 

It is, therefore, evident that the term depending on F^, has 
an influence of less than one per cent and that the term depending 
on VJ can be entirely neglected. 



THEORY OF THE INJECTOR 451 

For practical purposes we may calculate the weight of water 
delivered per pound of steam by the equation 

A 

y = _j_i u ^ (270) 

?4 - ?3 

This equation may be applied to any injector including double 
injectors with two steam-nozzles. 

The discussion just given shows that of the heat suppHed to 
an injector only a very small part, usually less than one per cent, 
is changed into work. When used for feeding a boiler, or for 
similar purposes, this is of no consequence, because the heat 
not changed into work is returned to the boiler and there is no 
loss. 

For example^ if dry steam is supplied to the injector at 120 
pounds by the gauge or 134.7 pounds absolute, if the supply- 
temperature of the water is 65° F., and if the dehvery-temperature 
is 165° F., then the water pumped per pound of steam is 

r, + J, — ^4 867. s + S2I.I — \\x.\ , 

y = -^ ^ ^' = — '-^ ^ 7^^^^— = 10.5 pounds. 

^4 - ?3 I33-I - 33-i6 

From the conservation of energy we have been able to devise 
an equation for the weight of water delivered per pound of 
steam; from the conservation of momenta we can find the relation 
of the velocities. 

The momentum of one pound of steam issuing from the steam- 
nozzle with the velocity F, is F, -^ g\ the momentum of y 
pounds of water entering the combining-tube with the velocity 
VJ is >'F„' ^ ^; and the momentum of i -f >' pounds of water 
at the smallest section of the delivery-tube is (i -^ y) Vu> -^ g- 
Equating the sum of the momenta of water and steam before 
mingling to the momentum of the combined water and steam 
in the delivery-tube, 

■Vs + yVJ = (I +y) F,, (270) 

This equation can be used to calculate any one of the velocities 
provided the other two can be determined independently. Unfor- 



452 INJECTORS 

tunately there is some uncertainty about all of the velocities so 
that the proper sizes of the orifices and of the forms and propor- 
tions of the several members of an injector have been determined 
mainly by experiment. The best exposition of this matter is 
given by Mr. Strickland Kneass,* who has made many experi- 
ments for William Sellers & Co. The practical part of what 
follows is largely drawn from his work. 

Velocity of the Steam-jet. — Equation (269) gives 

^. = 1^ (^/l - -^^2 + ?l - ^2) I ) • • (272) 

where r^ and q^ are the heat of vaporization and the heat of the 
liquid of the supply of steam at the pressure p^, and r^ and q^ 
are corresponding quantities at the pressure p^ for that section 
of the tube for which the velocity is calculated; x^ is the quality 
of the steam at the pressure p^ (usually 0.98 to unity) and x^ is 
the quality at the pressure p^ to be calculated by aid of the 
equation 

^^ 4- (9 = ^^^ + d . 

rp ' \ rp ^ 2' 

Here T^ and T^ are the absolute temperatures corresponding to 
the pressures p^ and p^, and 0^ and 0^ are the entropies of the 

liquid at the same pressure. Also — is the mechanical equivalent 

Ji. 

of heat and g is the acceleration due to gravity. 

Some steam-nozzles for injectors are simple converging orifices 
and others have a throat and a diverging portion. It will be 
found in all cases including double injectors, that the pressure 
beyond the steam- nozzle is less than half the pressure causing 
the flow, and consequently the pressure at the narrowest part 
of the steam-nozzle and also the velocity at that place, depend 
only on the initial pressure. As was developed in the preceding 
chapter, the pressure and velocity at any part of an expanding 
nozzle depend on the ratio of the area at that part to the throat 
area, and are consequently under control. Also, as was empha- 

* Practice and Theory of the Injector, J. Wiley & Sons. 



VELOCITY OF THE STEAM-JET 453 

sized by Rosenhain's experiments, the steam will expand and 
gain velocity beyond the nozzle, if it escapes at a pressure higher 
than the back-pressure. For an injector this last action is 
influenced by the fact that the jet from the steam-nozzle mingles 
with water and is rapidly condensed. Some injector makers 
use larger tapers than those recommended in the preceding 
chapter for expanding nozzles. The throat pressure may be 
assumed to be about 0.6 of the initial pressure; with the informa- 
tion in hand it is probably not worth while to try to make any 
allowance for friction. 

The calculation of the area at the throat of a steam nozzle by 
the adiabatic method will be found fairly satisfactory; the calcu- 
lation of the final velocity of the steam will probably not be 
satisfactory, as complete expansion in the nozzle seldom takes 
place, but it is easy to show that the velocity is sufficient to 
account for the action of the instrument. 

For example, the velocity in the throat of a nozzle under the 
pressure of 120 pounds by the gauge or 134.7 pounds absolute is 

^.= I ^ (^/i - ^2^ + ?i - ?2) r 

= !2 X 32.2 X 778 (867.5 - 0.967X894.6 H-32I. I -282.7)1^ 
= 1430 feet per second, 

having for x^ 

^2= 7^(^ + <^i - ^2)= j-^ (1-0719 + 0-5032 - 0.4546) 
= 0.967, 

provided that p^ = o.6p^ = 80.8 pounds absolute. 

If, however, the pressure at the exit of an expanded nozzle is 
14.7 pounds absolute, then 

^3 = 7Tb-^(i-°7i9 +0.5032 -0.3125) =0.877, 
1.4390 

and 

V,= I2X 32.2X778 (867.5 -0.8775 X966.3-f 321. 1 -i8o.3)(^ 
= 2830 feet per second. 



454 INJECTORS 

which is nearly twice that just calculated for the velocity at the 
smallest section of the steam-nozzle. Since there is usually a 
vacuum beyond the steam-nozzle, the final steam velocity is 
likely to be considerably larger, but this computed velocity will 
suffice for explaining the dynamics of the case. 

Velocity of Entering Water. — The velocity of the water in 
the combining-tube where it mingles with the steam depends on 
(a) the lift or head from the reservoir to the injector, (b) the 
pressure (or vacuum) in the combining-tube, and (c) on the 
resistance which the water experiences from friction and eddies 
in the pipe, valves, and passages of the injector. The first of 
these can be measured directly for any given case; for example, 
where a test is made on an injector. In determining the pro- 
portions of an injector it is safe to assume that there is neither 
lift nor head for a non-lifting injector, and that the lift for a 
lifting-injector is as large as can be obtained with certainty in 
practice. The lift for an injector is usually moderate, and 
seldom if ever exceeds 20 feet. 

The vacuum in the combining-tube may amount to 22 or 24 
inches of mercury, corresponding to 25 or 27 feet of water; that 
is, the absolute pressure may be 3 or 4 pounds per square inch. 
The vacuum after the steam and water are combined appears 
to be limited by the temperature of the water; thus, if the tem- 
perature is 165° F., the absolute pressure cannot be less than 
5.3 pounds. But the final temperature is taken in the delivery- 
pipe after the water and condensed steam are well mixed and are 
moving with a moderate velocity. 

The resistance of friction in the pipes, valves, and passages 
of injectors has never been determined ; since the velocity is high 
the resistance must be considerable. 

If we assume the greatest vacuum to correspond to 27 feet of 
water, the maximum velocity of the water entering the combining- 
tube will not exceed 

\^2gh = V2 X 32.2 X 27 = 42 feet. 

If, on the contrary, the effective head producing velocity is as 
small as 5 feet, the corresponding velocity will be 



SIZES OF THE ORIFICES 455 



V2 X 32.2 X 5 = 18 feet. 

It cannot be far from the truth to assume that the velocity of 
the water entering the combining-tube is between 20 and 40 
feet per second. 

Velocity in the Delivery-tube. — The velocity of the water in 
the smallest section of the delivery-tube may be estimated in two 
ways; in the first place it must be greater than the velocity of 
cold water flowing out under the pressure in the boiler, and in the 
second place it may be calculated by aid of equation (271), 
provided that the velocities of the entering steam and water are 
determined or assumed. 

For example, let it be assumed that the pressure of the steam 
in the boiler is 120 pounds by the gauge, and that, as calculated 
on page 451, each pound of steam delivers 10.5 pounds of water 
from the reserv^oir to the boiler. As there is a good vacuum in 
the injector we may assume that the pressure to be overcome is 
132 pounds per square inch, corresponding to a head of 

132 X 144 -, ^ 

.^ , = 305 feet. 
02.4 

Now the velocity of water flowing under the head of 305 feet is 
'V2gh = V2 X 32.2 X 305 = 140 feet per second. 

The velocity of steam flowing from a pressure of 120 pounds 
by the gauge through a diverging-tube with the pressure equal 
to that of the atmosphere at the exit has been calculated to be 
2830 feet per second. Assuming the velocity of the water enter- 
ing the combining-tube to be 20 feet, then by equation (271) 
we have in this case 

I + y I 4- 10.5 

this velocity is sufficient to overcome a pressure of about 470 
pounds per square inch if no allowance is made for friction or 
losses. 

Sizes of the Orifices. — From direct experiments on injectors as 
well as from the discussion in the previous chapter, it appears 



456 INJECTORS 

that the quantity of steam delivered by the steam-nozzle can be 
calculated in all cases by the method for the flow of steam, 
through an orifice, assuming the pressure in the orifice to be -^^ 
of the absolute pressure above the orifice. 

Now each pound of steam forces y pounds of water from the 
reservoir to the boiler; consequently if w pounds are drawn from 
the reservoir per second the injector will use w ^ y pounds of 
steam per second. 

The specific volume of the mixture of water and steam in the 
smallest section of the steam-nozzle is 

where x^ is the quality, u^ is the increase of volume due to vapor- 
ization, and o" is the specific volume of the water. The volume 
of steam discharged per second is 



— ^> 

y 

and the area of the orifice is 

where F^ is the velocity at the smallest section. 

For example, for a flow from 134.7 pounds absolute to 80.8 
pounds absolute x^ is 0.9670 and Vg is 1430 feet, as found on 
page 453. Again, for an increase of temperature from 65° F. 
to 165° F., the water per pound of steam is 10.5. Calculating 
the specific volume at 80.8 pounds, we have 
v., = x^u^ -f- cr = 0.967 (5.38 — 0.016) -}- 0.016 = 5.20 cubic feet. 

If the injector is required to deliver 1200 gallons an hour, or 

1200 X 2^1 X 62.4 „ 
^ ^± == 2.78 

1728 X 60 X 60 ' 

pounds per second, the area of the steam-nozzle must be 

WV„ 2.78 X 5.20 . r ^ 

a, = -—-/- = — = 0.000062 square feet. 

yV, 10.5 X 1430 

The corresponding diameter is 0.420 of an inch, or 10.6 milli- 
metres. 



SIZES OF THE ORIFICES 



457 



In trying to determine the size of the orifice in the delivery- 
tube we meet with two serious difficulties: we do not know the 
velocity of the stream in the smallest section of the delivery- 
tube, and we do not know the condition of the fluid at that place. 
It has been assumed that the steam is entirely condensed by 
the water in the combining-tube before reaching the delivery- 
tube, but there may be small bubbles of uncondensed steam still 
mingled with the water, so that the probable density of the 
heterogeneous mixture may be less than that of water. Since 
the pressure at the entrance to the delivery-tube is small, the 
specific volume of the steam is very large, and a fraction of a 
per cent of steam is enough to reduce the density of the steam 
to one-half. Even if the steam is entirely condensed, the air 
carried by the water from the reservoir is enough to sensibly 
reduce the density at the low pressure (or vacuum) found at the 
entrance to the delivery-tube. 

If V^ is the probable velocity of the jet at the smallest section 
of the delivery-tube, and if d is the density of the fluid, then the 
area of the orifice in square feet is 

for each pound of steam mingles with and is condensed by y 
pounds of water and passes with that water through the delivery- 
tube; w, as before, is the number of pounds of water drawn from 
the reservoir per second. 

For example, let it be assumed that the actual velocity in the 
delivery-tube to ov^ercome a boiler-pressure of 120 pounds by the 
gauge is 150 feet per second, and that the density of the jet is 
about 0.9 that of water; then with the value oi w = 2.78 and y = 
10.5, we have 

Wi+y) 2.78 X II. 5 . . 

a,r = — „ , = — = 0.000361 sq. ft. 

V,,dy 150 X 0.9 X 62.4 X 10.5 ^ ^ 

The corresponding diameter is 0.257 of an inch, or 6.5 milli- 
metres. If this calculation were made with the velocity 266 
(computed for expansion to atmospheric pressure) and with 



458 INJECTORS 

clear water the diameter would be only 0.183 of 2,n inch; this is 
to be considered rather as' a theoretic minimum than as a prac- 
tical dimension. 

Steam-nozzle. — The entrance to the steam-nozzle should be 
well rounded to avoid eddies or reduction of pressure as the 
steam approaches; in some injectors, as the Sellers' injector, 
Fig. 92, the valve controlling the steam supply is placed near 
the entrance to the nozzle, but the bevelled valve-seat will not 
interfere with the flow when the valve is open. 

It has already been pointed out that the steam-nozzle may 
advantageously be made to expand or flare from the smallest 
section to the exit. The length from that section to the end may 
be between two and three times the diameter at that section. 

Consider the case of a steam-nozzle supplied with steam at 
120 pounds boiler-pressure: it has been found that the velocity 
at the smallest section, on the assumption that the pressure is 
then 80.8 pounds, is 1430 feet per second, and that the specific 
volume is 5.20 cubic feet. If the pressure in the nozzle is 
reduced to 14.7 pounds, at the exit, the velocity becomes 2830 
feet per second, the quality being x^ = 0.8775. The specific 
volume is consequently 

V^ = ^2^2 + O- = 0.877 (26.66 — 0.016) + 0.016 = 23.4 CU. ft. 

The areas will be directly as the specific volumes and inversely 
as the velocities, so that for this case we shall have the ratio of 
the areas 

5.20: 23.4 



Q i = I- 2.27; 

2830: 1430 

and the ratio of the diameters will be 

Vi • V2.27 = i: 1.5. 

Combining-tube. — There is great diversity with different 
injectors in the form and proportions of the combining-tube. 
It is always made in the form of a hollow converging cone, 
straight or curved. The overflow is commonly connected to a 
space between the combining-tube and the delivery-tube; it is. 



EFFICIENCY OF THE INJECTOR 459 

however, sometimes placed beyond the delivery-tube, as in the 
Sellers' injector, Fig. 92. In the latter case the combining- and 
delivery- tuhes may form one continuous piece, as is seen in the 
double injector shown by Fig. 93. 

The Delivery-tube. — This tube should be gradually enlarged 
from its smallest diameter to the exit in order that the water in it 
may gradually lose velocity and be less affected by the sudden 
change of velocity where this tube connects to the pipe leading 
to the boiler. 

It is the custom to rate injectors by the size of the delivery- 
tube; thus a No. 6 injector may have a diameter of 6 mm. at 
the smallest section of the delivery-tube. 

Mr. Kneass found that a delivery-tube cut off short at the 
smallest section would deliver water against 35 pounds pressure 
only, without overflowing; the steam-pressure being 65 pounds. 
A cylindrical tube four times as long as the internal diameter, 
under the same conditions would deliver only against 24 pounds. 
A tube with a rapid flare delivered against 62 pounds, and a 
gradually enlarged tube delivered against 93 pounds. 

If the delivery-tube is assumed to be filled with water without 
any admixture of steam or air, then the relative velocities at 
different sections may be assumed to be inversely proportional 
to the corresponding areas. This gives a method of tracing the 
change of velocity of the water in the tube from its smallest 
diameter to the exit. 

A sudden change in the velocity is very undesirable, as at the 
point where the change occurs the tube is worn and roughened, 
especially if there are solid impurities in the water. It has been 
proposed to make the form of the tube such that the change of 
velocity shall be uniform until the pressure has fallen to that in 
the delivery-pipe; but this idea is found to be impracticable, as 
it leads to very long tubes with a very wide flare at the end. 

Efficiency of the Injector. — The injector is used for feeding 
boilers, and for little else. Since the heat drawn from the boiler 
is returned to the boiler again, save the very small part which 
is changed into mechanical energy, it appears as though the 



460 



INJECTORS 



efficiency was perfect, and that one injector is as good as another 
provided that it works with certainty. We may almost consider 
the injector to act as a feed-water heater, treating the pumping 
in of feed-water as incidental. It has already been pointed out 




Fig. 92- 

on page 450 that the kinetic energy of the jet in the delivery- 
tube is less than one per cent of the energy due to the condensa- 
tion of the steam. On this account the injector is used wherever 
cold water must be forced into a boiler, as on a locomotive, or 
when sea-water is supplied to a marine boiler. Considering 
only the advantage of supplying hot water to the boiler, it 
almost seems as though the more steam an injector uses the 
better it is. Such a view is erroneous, as it is often desirable 
to supply water without immediately reducing the steam- 
pressure and then it is necessary to use as little steam as may be. 
It is, however, true that simplicity of construction and certainty 
of action are of the first importance in injectors. 

Lifting Injector. — The injector described at the beginning of 



DOUBLE INJECTORS 461 

this chapter was placed so that water from the reservoir would 
run in under the influence of gravity. When the injector is 
placed higher than the reservoir a special device is provided for 
lifting the water to start the injector. Thus in the Sellers' 
injector, Fig. 92, there is a long tube which protrudes well into 
the combining-tube when the valves w and x are both closed. 
When the rod B is drawn back a little by aid of the lever H the 
valve w is opened, admitting steam through a side orifice to the 
tube mentioned. Steam from this tube drives out the air in 
the injector through the overflow, and water flows up into the 
vacuum thus formed, and is itself forced out at the overflow. 
The starting-lever H is then drawn as far back as it will go, 
opening the valve x and supplying steam to the steam-nozzle. 
This steam mingles with and is condensed by the water and 
imparts to the water sufficient velocity to overcome the boiler- 
pressure. Just as the lever H reaches its extreme position it 
closes the overflow valve K through the rod L and the crank at R. 

Since lifting-injectors may be supplied with water under a 
head, and since a non-lifting injector when started will lift 
water from a reservoir below it, or may even start with a small 
lift, the distinction between them is not fundamental. 

Double Injectors. — The double injector illustrated by Fig. 93, 
which represents the Korting injector, consists of two complete 
injectors, one of which draws water from the reservoir and 
delivers it to the second, which in turn delivers the water to the 
boiler. To start this injector the handle A is drawn back to 
the position B and opens the valve supplying steam to the 
lifting- injector. The proper sequence in opening the valves 
is secured by the simple device of using a loose lever for joining 
both to the valve-spindle; for under steam-pressure the smaller 
will open first, and when it is open the larger wfll move. The 
steam-nozzle of the lifter has a good deal of flare, which tends 
to form a good vacuum. The lifter first delivers water out at 
the overflow with the starting lever at B\ then that lever is pulled 
as far as it will go, opening the valve for the second injector or 
forcer, and closing both overflow valves.. 



462 



INJECTORS 



Self-adjusting Injectors. — In the discussions of injectors 
thus far given it has been assumed that they work at full capac- 
ity, but as an injector must be able to bring the water-level 
in a boiler up promptly to the proper height, it will have much 
more than the capacity needed for feeding the boiler steadily. 
Any injector may be made to work at a reduced capacity by 
simply reducing the opening of the steam-valve, but the limit 




Fig. 93. 



of its action is soon reached. The limit may be extended some- 
what by partially closing the water-supply valve and so limiting 
the water-supply. 

The original Giffard injector had a movable steam-nozzle to 
control the thickness of the sheet of water mingling with the 
steam, and also had a long conical valve thrust into the steam- 
nozzle by which the effective area of the steam- jet could be regu- 
lated. Thus both water and steam passages could be controlled 
without changing the pressures under which they were supplied, 
and the injector could be regulated to work through a wide 
range of pressures and capacities. The main objection was 
that the injector was regulated by hand and required much 
attention. 



SELF-ADJUSTING INJECTORS 463 

In the Sellers' injector, Fig. 92, the regulation of the steam- 
supply by a long cone thrust through the steam-nozzle is 
retained, but the supply of water is regulated by a movable 
combining-tube, which is guided at each end and is free to move 
forwards and backwards. At the rear the combining-tube is 
affected by the pressure of the entering water, and in front it is 
subjected to the pressure in the closed space O, which is in 
communication with the overflow space between the combining- 
tube and the delivery-tube, in this injector the space is only for 
producing the regulation of the water-supply by the motion of 
the combining-tube, as the actual overflow is beyond the 
delivery-tube at K. When the injector is running at any regular 
rate the pressures on the front and the rear of the combining-tube 
are nearly equal, and it remains at rest. When the starting- 
lever is drawn out or the steam-pressure increases, the inflowing 
steam is not entirely condensed in the combining-tube as it is 
during efficient action; lateral contraction of the jet therefore 
occurs when crossing the overflow chamber, causing a reduction 
of pressure in O, which causes the tube to move toward D and 
increase the supply of water. When the starting-lever is pushed 
inward, reducing the flow of steam, the impulsive effort is 
insufficient to force a full supply of water through the delivery- 
tube, and there is an overflow into the chamber O which pushes 
the combining-tube backwards and reduces the inflow of water. 
The injector is always started at full capacity by pulling the 
steam-valve wide open, as already described; after it is started 
the steam-supply is regulated at will by the engineer or boiler 
attendant, and the water is automatically adjusted by the movable 
combining-tube, and the injector will require attention only 
when a change of the rate of feeding the boiler is required on 
account of either a change in the draught of steam from the 
boiler, or a change of steam-pressure, for the capacity of the 
injector increases with a rise of pressure. 

A double injector, such as that represented by Fig. 93, is to a 
certain extent self-adjusting, since an increase of steam- pressure 
causes at once an increase in the amount of water drawn in by 



464 



INJECTORS 



the lifter and an increase in the flow of steam through the steam- 
nozzle of the forcer. Such injectors have a wide range of action 
and can be controlled by regulating the valve on the steam- 
pipe. 

Restarting Injectors. — If the action of any of the injector 
thus far described is interrupted for any reason, it is necessary to 

shut off steam and start the 
injector anew; sometimes the 
injector has become heated 
while its action is interrupted, 
and there may be difficulty in 
starting. To overcome this 
difficulty various forms of 
restarting injectors have been 
devised, such as the Sellers, 
Fig. 94. This injector has 
four fixed nozzles in line, the 
steam-nozzle 3, the draft-tube 
II, the combining-tube 2, 
and the delivery-tube at the 
bottom. There is also a slid- 
ing bushing 5 and an overflow 
valve 15. The steam-nozzle has a wide flare and makes a vacuum 
which draws water from the supply- tank under all conditions; the 
water passes through the draught-tube and out at the overflow 
until the condensation of steam in the combining-tube makes a 
partial vacuum that draws up the bushing 5 against the draught- 
tube and shuts off the passage to the overflow; the injector then 
forces water to the boiler. If the injector stops for any cause 
the bushing falls and the injector takes the starting position and 
will start as soon as supplied with water and steam. 

Self-acting Injector. — The most recent type of Sellers' injector 
invented by Mr. Kneass and represented by Fig. 95 is both self- 
starting and self-adjusting. It is a double injector with all the jets 
in one line; a, b, and c are the steam-nozzle, the combining-tube, 
and the delivery-tube of the forcer; the lifter is composed of the 




Fig. 



INJECTORS 



465 




466 INJECTORS 

annular steam-nozzle d, and the annular delivery- tube e, sur- 
rounding the nozzle a. The proportions are such that the lifter 
can always produce a suction in the feed-pipe even when there 
is a discharge from the main steam-nozzle, and it is this fact 
that establishes the restarting feature. When the feed-water 
rises to the tubes it meets the steam from the lifter-nozzle and 
is forced in a thin sheet and with high velocity into the combining- 
tube of the forcer, where it comes in contact with the main 
steam-jet, and mingling with and condensing it, receives a 
high velocity which enables it to pass the overflow orifices and 
proceed through the delivery-tube to the boiler. 

Like any double injector, the lifter and forcer have a con- 
siderable range of action through which the water is adjusted 
to the steam-supply; but there is a further adjustment in this 
injector, for when a good vacuum is established in the space 
surrounding the combining-tube, water can enter through the 
check- valve /, and flowing through the orifices in the combin- 
ing-tube mingles with the jet in it, and is forced with that jet 
into the boiler. 

The steam- valve is seated on the end of the lifter-nozzle, 
and it has a protruding plug which enters the forcer-nozzle. 
When the valve is opened to start the injector, steam is sup- 
plied first to the starter, and soon after, by withdrawing the 
plug, to the forcer: If the steam is dry the starting-lever 
may be moved back promptly; if tHere is condensed water in 
the steam-pipe, the starting-handle should be moved a little 
way to first open the valve of the lifter, and then it is drawn 
as far back as it will go, as soon as water appears at the over- 
flow. The water-supply may be regulated by the valve g, 
which can be rotated a part of a turn. The minimum delivery 
of the injector is obtained by closing this valve till puffs of 
steam appear at the overflow, and then opening it enough 
to stop the escape of steam. 

When supplied with cold water this injector wastes very 
little in starting. If the injector is hot or is filled with hot 
water when started, it will waste hot water till the injector is 



EXHAUST STEAM INJECTORS 



467 



cooled by the water from the feed-supply, and will then work 
as usual. If air leaks into the suction-pipe or if there is any 
other interference with the normal action, the injector wastes 
water or steam till normal conditions are restored, when it 
starts automatically. 

Exhaust Steam Injectors. — Injectors supplied with ex- 
haust-steam from a non-condensing engine can be used to 
feed boilers up to a pressure of about 80 pounds. Above 
this pressure a supplemental jet of steam from the boiler must 
be used. Such an injector, as made by Schaffer and Buden- 
berg, is represented by Fig. 96; when ^xviamst s.-^'lk'^ 

used with low boiler-pressure this in- 
jector has a solid cone or spindle in- 
stead of the live-steam nozzle. To 
provide a very free overflow the com- 
bining-tube is divided, and one side is 
hung on a hinge and can open to give 
free exit to the overflow^ when the 
injector is started. When the injector 
is working it closes down into place. 
The calculation for an exhaust-steam 
injector shows that enough velocity 
may be imparted to the water in the 
delivery-tube to overcome a moderate 
boiler-pressure. 

For example, an injector supplied with steam at atmospheric 
pressure, and raising the feed-water from 65° F. to 145° F., 
will draw from the reservoir 




Fig. 96. 



_ ^1 + gi - g4 _ 966.3 + 180.3 - 1 13-0 _ J 



2.9 



pounds of water per pound of steam. In this case as the steam- 
nozzle is converging we will use for computing the velocity the 
pressure 

0.6 X 14.7 = 8.8 pounds. 



468 INJECTORS 

This will give 

^2= ^2(^ + ^1- ^2)= 646.8(1.4390+0-3125- .2746) =954.6, 

consequently 



= V2 X 32.2 X 778 (966.3 + 180.3 - 954.6 - 155.3 = 1370. 

Assuming the velocity of the water entering the combining- 
tube will give for the velocity of the jet in the combining-tube 



136 feet. 



_ 1370 + 12.9 X 30 
I + 12.9 

This velocity is equivalent to that produced by a static pressure 

of 

136' X 62.4 

-f = 124 

64.4 X 144 

pounds absolute, or a gauge pressure of 109 pounds. No allow- 
ance is made for reduction of density by bubbles of steam in 
the combining-tube or for resistance of pipes and valves. If 




Fig. 97- 



such an injector can take advantage of further expansion either 
in the steam-nozzle or beyond, the velocity may be greater than 
that computed and a better action might ensue. 

Unless the exhaust-steam is free from oil its use for feeding 



WATER-EJECTOR 469 

the boiler with an exhaust-steam injector will result in fouling 
the boiler. 

Water-ejector. — Fig. 97 represents a device called a water- 
ejector, in which a small stream of water in the pipe M flowing 
from the reservoir R raises water from the reservoir i?" to the 
reservoir R'. 

Let one pound of water from the reservoir R draw y pounds 
from i?", and deliver i + ^ pounds to R'. Let the velocity of 
the water issuing from A he v; that of the water entering from 
R" be v^ at A^; and that of the water in the pipe O be v^. The 
equality of momenta gives 

V + yv^= {1 + y)v^ (275) 

Let X be the excess of pressure at M above that at A^ expressed 
in feet of water; then 

v' = 2g(H + x); 

V^ = 2g (h + x) 
Substituting in equation (275), 



\^H + X + y ^x = (i + )') V/z + X) 



Vh + X - Vh + X , ^. 

.-. y = -==^ -= — . . . (276) 

V h + X — ^ X 

It is evident from inspection of the equation (276) that y 
may be increased by increasing x; for example, by placing the 
injector above the level of the reservoir so that there may be a 
vacuum in front of the orifice A. 

Q 

If the weight G of water is to be lifted per second, then - 

y. 

pounds per second must pass the orifice A, G pounds the space 

at N, and (1 -f —) G pounds through the section at O; which, 

with the several velocities v, v^, and v^, give the data for the 
calculation of the required areas. 

Problem. — Required the calculation for a water-ejector 



470 INJECTORS 

to raise 1200 gallons of water an hour, H = g6 ft., h = 12 ft. 

.V = 4 ft. 

Vx = ^4 = 2; Vif 4- .T= Vioo = 10; \^h + x = V^i6 = 4; 



10 — 4 

y = 



The velocities are 



V =V2 X 32.2 X 100 = 80.25 feet per second; 
v^ =\^2 X 32.2 X 16 = 32.10 feet per second; 
v^ =\^2 X 32.2 X 4 = 16.05 f^^t per second. 
1200 gallons an hour = 0.04452 cubic feet per second. 
The areas are 

0.04452 o ., ^ 

^ ^ :ri^ — ^ 0.000185 square teet; 

3 X 80.25 ^ ^ ' 

4 X 0.04452 , o - . 
^ ^ 2 xi^ ^ 0.06185 square feet: 

' 3 X 32.10 

0.04452 . ^ 

a„ = — 7^^^^^ = 0.00277 square feet. 

16.05 

The diameters corresponding to the velocities v and v^ are 
d = 0.18 of an inch; 
d^ = 0.58 of an inch. 
The area a^ is of annular form, having the area 0.4 of a square 
inch. 

Ejector. — When the ejector is used for raising water where 
there is no advantage in heating the water, it is a very wasteful 
instrument. The efficiency is much improved by arranging 

the instrument as in Fig. 98, so 

that the steam-nozzle A shall deliver 

a small stream of water at a high 

velocity, which, as in the water- 

^^* ^ ■ ejector, delivers a larger stream at 

a less velocity. Each additional conical nozzle increases the 

quantity at the expense of the velocity, so that a large quantity 

of water may be lifted a small height. 




EJECTOR-CONDENSERS 471 

Ejectors are commonly fitted in steamships as auxiliary pumps 
in case of leakage, a service for which they are well fitted, since 
they are compact, cheap, and powerful, and are used only in 
emergency, when economy is of small consequence. 

Ejector-condensers. — When there is a good supply of cold 
condensing water, an exhaust-steam ejector, using all the 
steam from the engine, may be arranged to take the place of 
the air-pump of a jet-condensing engine. The energy of the 
exhaust-steam flowing from the cylinder of the engine to the 
combining-tube, where the absolute pressure is less and where 
the steam is condensed, is sufficient to eject the water and the air 
mingled with it against the pressure of the atmosphere, and thus 
to maintain the vacuum. 

For example, if the absolute pressure in the exhaust-pipe is 2 
pounds, and if the temperatures of the injection and the delivery 
are 50° F. and 97° F., then the water supplied per pound of 
steam will be about 20 pounds. If the pressure at the exit of 
the steam-nozzle can be taken as one pound absolute, the velocity 
of the steam- jet will be 1460 feet per second. If the water is 
assumed to enter with a velocity of 20 feet, the velocity of the 
water-jet in the combining-tube will be 88 feet, which can over- 
come a pressure of 50 pounds per square inch. 



CHAPTER XIX. 

STEAM-TURBINES. 

The recent rapid development of steam-turbines may be 
attributed largely to the perfecting of mechanical construction, 
making it possible to construct large machinery with the accuracy 
required for the high speeds and close adjustments which these 
motors demand. 

An adequate treatment of steam-turbines, including details of 
design, construction, and management, would require a separate 
treatise; but there is an advantage in discussing here the thermal 
problems that arise in the transformation of heat into kinetic 
energy, and the application of this energy to the moving parts 
of the turbine. For this purpose it is necessary to give attention 
to the action of jets of fluids on vanes and to the reaction of jets 
issuing from moving orifices, subjects that otherwise would 
appear foreign to this treatise. 

The fundamental principles of the theory of turbines are the 
same whether they are driven by water or by steam; but the use 
of an elastic fluid like steam instead of a- fluid like water, which 
has practically a constant density, leads to differences in the 
application of those principles. One feature is immediately 
evident from the discussion of the flow of fluids in Chapter XVII, 
namely, that ej^ceedingly high velocities are liable to be devel- 
oped. Thus, on page 444 it was found that steam flowing from 
a gauge pressure of 150 pounds per square inch into a vacuum 
of 26 inches of mercury (2 pounds absolute) through a proper 
nozzle, developed a velocity of 3500 feet per second, with an 
allowance of 0.15 for friction. This range of pressure corre- 
sponds to a hydraulic head of 

163 X 144 -^ 62.4 = 376 feet; 

472 



IMPULSE 473 

and such a head will give a velocity of 

V = V2 X 32.2 X 376 = 156 feet per second. 

But so great a hydraulic head or fall of water is seldom, if ever, 
applied to a single turbine, and would be considered inconvenient. 
One hundred feet is a large hydraulic head, yielding a velocity 
of 80 feet per second, and twenty-five feet yielding a velocity of 
40 feet per second is considered a very effective head. 

If heads of 300 feet and upward were frequent, it is likely 
that compound turbines would be developed to use them; except 
for relatively small powers, steam-turbines are always compound, 
that is, the steam flows through a succession of turbines which 
may therefore run at more manageable speeds. 

The great velocities that are developed in steam turbines, 
even when compounded, require careful reduction of clearances, 
and although they are restricted to small fractions of an inch 
the question of leakage is very important. Another feature in 
which steam turbines differ from hydraulic turbines is that 
steam is an elastic fluid which tends to fill any space to which it 
is admitted. The influence of this feature will appear in the 
distinction between impulse and reaction turbines. 

Impulse. — If a well formed stream of water at moderate 
velocity flows from a conical nozzle, on a flat plate it spreads 
over it smoothly in all directions and exerts a 
steady force on it. If the velocity of the stream ^^^ J 

is Fj feet per second, and if w pounds of water are ^^ 

discharged per second, the force will be very 
nearly equal to 

g 

Here we have the velocity in the direction of the jet changed 
from Fj feet per second to zero; that is, there is a retardation, or 
negative acceleration, of V^ feet per second; consequently the 
force is measured by the product of mass and the acceleration, 
g being the acceleration due to gravity. A force exerted by a 
jet or stream of fluid on a plate or vane is called an impulse. It 



474 STEAM-TURBINES 

is important to keep clearly in mind that we are dealing with 
velocity, change of velocity or acceleration, and force, and that 
the force is measured in the usual way. The use of a special 
name for the force which is developed in this way is unfortunate 
but it is too well established to be neglected. 

If the plate or vane, instead of remaining at rest, moves with 
the velocity of V feet per second, the change in velocity or negative 
acceleration will be V^ ~ V feet per second, and the force or 
impulse will be 

P =-{V,- V). 

o 

This force in one second will move the distance V feet and will 
do the work 

- (V,- V)V = - (VJ - V) . . . (276) 

o o 

foot-pounds. 

Since the vane would soon move beyond the range of the jet, 
it would be necessary, in order to obtain continuous action on a 
motor, to provide a succession of vanes, which might be mounted 
on the rim of a wheel. There would be, in consequence, waste 
of energy due to the motion of the vanes in a circle and to 
splattering and other imperfect action. 

If the velocity of the jet of water is high it would fail to spread 
fairly over the plate in Fig. 99, when it is at rest, and a crude 
motor of the sort mentioned would show a very poor efficiency. 
Now steam has exceedingly high velocity when discharged from 
a nozzle, and the jet is more easily broken, so that adverse influ- 
ences have even a worse effect than on water, and there is the 
greater reason for following methods which tend to avoid waste. 
Also, as pointed out on page 434, the nozzle must be so formed as 
to expand the steam down to the back pressure, or expansion 
will continue beyond the nozzle with further acceleration of the 
steam under unfavorable conditions. ' 

It is easy to show that the best efficiency of the simple action 
of a jet on a vane, which we have discussed, will be obtained by 
making the velocity V of the vane half the velocity F, of the jet. 



IMPULSE 



475 



For if we differentiate the expression (276) with regard to V 
and equate the differential coefficient to zero we shall have 

V,- 2F = o; V = iV,; 

and this value carried into expression (276) gives for the work 
on the vane 

*^ 1 ' 
4 g 

but the kinetic energy of the jet is 

1 w 

2 g 

so that the efficiency is 0.5. 

If the flat plate in Fig. 99 be replaced by a semi-cylindrical 
vane as in Fig. 99a, the direction of the stream will be reversed, 
and the impulse will be twice as great. If the 
vane as before has the velocity V the relative 
velocity of the jet with regard to the vane will 
be 

V^ — V Fig. 99a. 

and neglecting friction this velocity may be attributed to the 
water where it leaves the vane. This relative velocity at exit 
will be toward the rear, so that the absolute velocity will be 

V - (V,- V) = 2V - F,. 

The change of velocity or negative acceleration will be 

V, - (2F - FJ = 2 (F, - F), 

and the impulse is consequently 










P 


"^ /Tr 

= -.(F.- 


- V). 




The work of the 


impulse 


becomes 










w 
2 


.2 (F, - 


- F) F = 2 


1''' 


,v 


The 


maximum < 


occurs when 









d 
dV 


{V,V 


- p) 


= F, - 2 F 


= 


01 



■n ■ ■ (277) 



47< 



STEAM-TURBINES 



But this value introduced in equation (277) now gives 

2 g 

which is equal to the kinetic energy of the jet, and consequently 
the efficiency without allowing for losses appears to be unity. 

Certain water-wheels which work on essentially this principle 
give an efficiency of 0.85 to 0.90. The method in its simplest 
form is not well adapted to steam turbines, but this discussion 
leads naturally to the treatment of all impulse turbines now 
made. 

Reaction. — If a stream of water flows through a conical 
nozzle into the air with a velocity V^ as in Fig. 100, a force 




g 



(278) 



Fig. 



will be exerted tending to move the vessel 
from which the flow takes place, in the 
contrary direction. Here again w is the 
weight discharged per second, and g is the 
acceleration due to gravity. The force R 
is called the reaction, a name that is so 
commonly used that it must be accepted. 
Since the fluid in the chamber is at rest, the velocity V^ is that 
imparted by the pressure in one second, and is therefore an 
acceleration, and the force is therefore measured by the product 
of the mass and the acceleration. However elementary this may 
appear, it should be carefully borne in mind, to avoid future 
confusion. 

If steam is discharged from a proper expanding nozzle, which 
reduces the pressure to that of the atmosphere, its reaction will 
be very nearly represented by equation (278), but if the expansion 
is incomplete in the nozzle it will continue beyond, and the 
added acceleration will effect the reaction. . On the other hand, 
if the expansion is excessive there will be sound waves in the 
nozzle and other disturbances. 



GENERAL CASE OF IMPULSE 



477 



The velocity of the jet depends on the pressure in the chamber, 
and if it can be maintained, the velocity will be the same rela- 
tively to the chamber when the latter is supposed to move. The 
work will in such case be equal to the product of the reaction, 
computed by equation (278), and the velocity of the chamber. 
There is no simple way of supplying fluid to a chamber which 
moves in a straight line, and a reaction wheel supplied with 
fluid at the centre and discharging through nozzles at the cir- 
cumference is affected by centrifugal force. Consequently, 
as there is now no example of a pure reaction steam turbine, it 
is not profitable to go further in this matter. It is, however, 
important to remember that velocity, or increase of velocity, is 
due to pressure in the chamber or space under consideration, 
and is relative to that chamber or space. 

General Case of Impulse. — In Fig. loi let ac represent the 
velocity V^ of a jet of fluid, and let V represent the velocity of a 
curved vane ce. Then the 
velocity of the jet, relative 
to the vane is V^ equal 
to be. This has been drawn 
in the figure coincident 
with the tangent at the end 
of the vane, and in general 
this arrangement is desir- 
able because it avoids 
splattering. 

If it be supposed that 
the vane is bounded at 
the sides so that the steam 
cannot spread laterally and 

if friction can be neglected, the relative velocity V^ may be 
assumed to equal F2. Its direction is along the tangent at 
the end e of the vane. The absolute velocity V^ can be found 
by drawing the parallelogram efgh with ef equal to F, the 
velocity of the vane. 

The absolute entrance velocity F, can be resolved into the 




Fig. ioi. 



478 STEAM-TURBINES 

two components ai and ic, along and at right angles to the direc- 
tion of motion of the vane. The former may be called the 
xelocity of flow, Vf, and the latter the velocity of whirl, Vy,. 
In like manner the absolute exit velocity may be resolved into 
the components ek and kg, which may be called the exit velocity 
of whirl F/, and the exit velocity of flow, V/. 

The kinetic energy corresponding to the absolute exit velocity 
V^ is the lost or rejected energy of the combination of jet and 
vane, and for good efficiency should be made small. The exit 
velocity of whirl in general serves no good purpose and should 
be made zero to obtain the best results. 

The change in the velocity of whirl is the retardation or nega- 
tive acceleration that determines the driving force or impulse; 
and the change in the velocity of flow in like manner produces 
an impulse at right angles to the motion of the vane, which in 
a turbine is felt as a thrust on the shaft. 

Let the angle acd which the jet makes with the line of motion 
of the vane be represented by a, and let /? and 7 represent the 
angles bed and Ich which the tangents at the entrance and exit of 
the vane make with the same line. 

The driving impulse is in general equal to 

P =-(V,, - VJ) ; (279) 



ft 



and the thrust is equal to 



T=-(V,-V/) (280) 

If there is no velocity of whirl at the exit the impulse becomes 

7/1 
p = _F^ cos a (281) 

o 

In any case the thrust is 

r = - (F, sin a - F3 sin 7) . • • (282) 



The work delivered to the vane per second is 



W=-VV, COS a, (283) 

g 



GENERAL CASE OF IMPULSE 



479 



and since the kinetic energy of the jet is wF/ -^ 2g the effi- 
ciency is 

V 
e = 2 ■— cos a (284) 

To find the relations of the angles a, /?, and 7, we have from 
inspection of Fig. 102 in which el is equal to ef, 

Fj sin a = Fj sin /? . . .' . . . (285) 



P^ = F2 cos 7 . . . . 
V ^ Vj^ cos a — Fg cos /?; 



(286) 



from which 



Fj cos a 



J, sm a „ 

F, ■ . , cos ^■■ 



sm a cos 7 



and 



sin /? *' sin /? 

sin /5 cos a — cos ,5 sin a = sin a cos 7 

sin {^3 — ci) = sin o: cos 7 

The equations given above may 
be applied to the computation 
of forces, work, and efficiency 
when w pounds of fluid are dis- 
charged from one or several noz- 
zles and act on one or a number 
of vanes ; that is, they are directly 
applicable to any simple impulse 
turbine. 

Example. Let Fj, the velocity 
of discharge, be 3500 feet per 
second as computed for a nozzle 
on page 444, and let a = 7 = 30°. By equation (287) 

sin (,/9 — a) = sin a: cos 7 = 0.5 X 0.866 = 0.433; 
.-. 3 - a = 25 40'; /9 = 55° 40' 



(287) 




Vu: 



F. 



. sm a 

' sin /? 



3500 



0-5 



2020 



0.866 

F = F2 cos 7 = 2020 X 0.866 = 1750 
^ = 2 X 1750 X 0.866 ^ 3500 = 0.866. 



48o 



STEAM-TURBINES 



No Axial Thrust. 




Fig. 103. 



The builders of impulse steam-turbines 
attribute much importance to 
avoiding axial thrust, which can 
be done by making the entrance 
and exit angles of the vanes 
equal, provided that friction 
and other resistances can be 
neglected. This is evident from 
equation (280), provided that 
7 is made equal to /? and V^ 
equal to V^, and also that V^ 
sin a is replaced by V^ sin /?. 
Or the same conclusion can be 
drawn from Fig. 103 because 
in this case 



at 



V^ sin a 



V^ sin f^ 



F, sin 7 = hi, 



and consequently there is no axial retardation. 

The de Laval turbine has only one set of nozzles which expand 
the steam at once to the back pressure, and consequently the 
velocity of the vanes is very high and even with small wheels 
it is difficult to balance them satisfactorily. This difficulty is 
met by the use of a flexible shaft, and consequently axial thrust 
is likely to be troublesome; as a matter of fact the turbine is so 
arranged that the axial force (if there is any) shall be a pull. 
The importance of avoiding axial thrust in other types of impulse 
turbines does not appear to be so great, and in some cases axial 
thrust may be an advantage, for example in marine propulsion. 

If 7 is made equal to /? in equation (287) we have 

sin /9 cos a — cos /9 sin a 



sm a cos 



cot 1^ = i cot a 



(288) 



and from inspection of Fig. loi it is evident that V is half of the 
velocity of whirl or 

(289) 



F = i 



V^ COS, (X 



DESIGN OF A SIMPLE IMPULSE-TURBINE 481 

If this value is carried into equations (28^) and (284) the 

work and etficiency become 

It' 
W = h — V^ cos a (290) 

o 

and 

e = cos^ a (291) 

This freedom from axial thrust appears to be purchased 
dearly unless the accompanying reduction of velocity of the 
wheel is to be considered also of importance. 

Example. If as in the preceding case the velocity of discharge 
is 3500 feet per second, and if a is 30°, we have now the following 
results, 

cot;9 = I cot a = }y X 1.732 = 0.866 .'. ^3 = 49° 10' 
V = i V\ cos a' = J X 3500 X 0.866 = 1515 
e = cos" 30° = 0.75. 

Effect of Friction. — The direct effect of friction is to reduce 
the exit velocity from the vane; resistance due to striking the 
edges of the vanes, splattering, and other irregularities, will 
reduce the velocity both at entering and leaving. The effect of 
friction and other resistances is two-fold; the effect is to reduce 
the efficiency of the wheel by changing kinetic energy into heat, 
and to reduce the velocity at which the best efficiency will be 
obtained. There does not appear to be sufficient data to permit 
of a quantitative treatment of this subject. Small reductions 
from the speed of maximum efficiency will have but small effect. 

The question as to what change shall be made in the exit 
angle (if any) on account of friction will depend on the relative 
importance attached to avoiding velocity of whirl and axial 
thrust. If the latter is considered to be the more important, 
then 7 should be made somewhat larger so that the exit velocity 
of flow may be equal to the entrance velocity of flow. But if it 
is desired to make the exit velocity of whirl zero, then 7 should be 
somewhat decreased. 

Design of a Simple Impulse Turbine. — The following compu- 
tation may be taken to illustrate the method of applying the 



482 STEAM-TURBINES 

foregoing discussion to a simple impulse turbine of the de Laval 
type. 

Assume the steam-pressure on the nozzles to be 150 pounds 
gauge and that there is a vacuum of 26 inches of mercury ; required 
the principal dimension of a turbine to deliver 150 brake horse- 
power. 

The computation on page 444 for a steam-nozzle under these 
conditions gave for the velocity of the jet, allowing 0.15 for 
friction, V^ = 3500 feet per second. The throat pressure was 
taken to be 96 pounds absolute, giving a velocity at the throat 
of 1480 feet per second. The dryness factor was 0.965 at the 
throat; at the exit this factor was 0.833 ^^^ 0.15 friction and for 
adiabatic expansion was 0.790. 

The thermal efficiency for adiabatic expansion with no allow- 
ance for friction or losses whatsoever, as for an ideal non-con- 
ducting engine, is given by equation (144) page 136 as 

e = i 2-^ = 1 — -— ^^ ^ — = 0.262 ; 

^1 + ?i - ?2 ^56.0 + 337-6- 94.3 

the corresponding heat consumption is 

42.42 -^ 0.262 = 162, 

by the method on page 144. 

Let the angle of the nozzle be taken as 30° as on page 479, 
then the angle /? becomes 49° 10', the efficiency is 0.75 and the 
velocity of the vanes must be 151 5 feet per second. 

Suppose that ten per cent be allowed for friction and resistance 
in the vanes, and that the friction of the bearings and gears is 
ten per cent; then, remembering that 0.15 was allowed for the 
friction in the nozzle, and that the efficiency deduced from the 
velocities is 0.75, the combined efficiency of the turbine should 
be 

0.262 X 0.75 X 0.85 X 0.9 X 0.9 = 0.135; 

which corresponds to 

42.42 ^ 0.135 = 314 B.T.U. 

per horse-power per minute. 



DESIGN OF A SIMPLE IMPULSE TURBINE 



483 



Now it costs to make one pound of steam at 150 pounds by 
the gauge or 165 pounds absolute, from feed water at 126° F. 
(2 pounds absolute) 

^ + 9i - ^2 = 856.0 + 337.6 - 94.3 = 1099 B.T.U., 

consequently 314 b.t.u. per horse-power per minute correspond 
to 

314 X 60 -^ 1099 = 17.2 

pounds of steam per horse-power per hour. 

The total steam per hour for 150 horse-power appears to be 

150 X 17.2 = 1580. 

If the nozzle designed on page 444 be taken it appears that 
five would not be sufficient, as 
each would deliver only 500 
pounds of steam per hour. But 
if allowance be made for a mod- 
erate overload, six could be 
supplied. 

Not uncommonly turbines of 
this type are run under speed as 
a matter of convenience. Sup- 
pose, for example, the speed of 
the vanes is only 0.3 of the 
velocity of whirl, instead of 
0.5; that is, in this case take 
V = 1050. 

This case is represented by Fig. 104, from which it is evident 
that 

Vj. = V/ = at = V^ sin 30° = 3500 X 0.5 = 1750 

F«,= Fj cos 30^ = 3500 X 0.86 = 3030 

tan p = ai ^ id = 1750-J- (3030 — 1050) = 0.884 

/3 = 41° 3°'- 
The two triangles aid and elh are equal, and 
le = id = 3030 — 1050 = 1980; 




Fig. 104. 



484 STEAM-TURBINES 

consequently the exit velocity of whirl is 

Wf = ek = 1050 — 1980 = — 930. 

Consequently the work delivered to the vane is 

-PV = -[3030 - (- 930)] 1050=- 3960 X 1050 

00 o 

w 
= 416000 — • 

g 

But the kinetic energy is wV^^ -^ 2g, so that the efficiency is 

2 

416000 X 2 -r- 3500 = 0.68. 

The combined efficiency of the turbine therefore becomes 

0.262 X 0.68 X 0.85 X 0.9 X 0.9 = 0.123 
instead of 0.135; ^-nd the heat consumption becomes 
42.42 -f- 0.123 == 342 B.T.U. 

per horse-power per minute; and the steam consumption increases 

to 

342 X 60 -^ 1099 = 18.7 

pounds per horse- power per hour. The total steam per hour 
appears now to be about 

18.7 X 150 = 2800, 

so that six nozzles like that computed on page 444 would give 
only a margin for governing. 

If the turbine be given twelve thousand revolutions per minute 
the diameter at the middle of the length of the vanes will be 

D = 1050 X 12 X 60 -^ (3.14 X 12000) = 20 inches. 

The computation on page 444 gave for the exit diameter of 
the nozzle 1.026 inches, and as the angle of inclination to the 
plane of the wheel is 30°, the width of the jet at that plane 
would be twice the exit diameter or somewhat more, due to the 
natural spreading of the jet. The radial length of the vanes 
may be made somewhat greater than an inch, perhaps i^^ inches. 
The circumferential space occupied by the six jets will be about 



TESTS ON A DE LAVAL TURBINE 



485 



12J inches out of 62.8 inches (the perimeter), or somewhat less 
than one-fifth. The section of the nozzle is shown by 





Fig. 105. 

Fig. 105, and the form of the vanes may be like Fig, 106. 
In this case the thickness of a vane is made half the space 
from one vane to the next, or one-third the 
pitch from vane to vane. The normal width 
of the passage is made constant, the face of one 
vane and the back of the next vane being struck 
from the same centre. The form and spacing 
of vanes can be determined by experience only 
and appears to depend largely on the judgment 
of the designer. In deciding on the axial width pio. jo6 

of the vanes it must be borne in mind that 
increasing that width increases the length and therefore the 
friction of the passage; but that on the other hand, decreasing 
the width increases the curvature of the passage which may be 
equally unfavorable. Sharply curved passages also tend to 
produce centrifugal action, by which is meant now a tendency to 
crowd the fluid toward the concave side which tends to raise 
the pressure there, and decreases it at the convex side. Mr. 
Alexander Jude,* for a particular case with a steam velocity of 
1000 feet per second, computes a change of pressure from 100 to 
107. 1 pounds on the concave side and a fall to 93.4 on the convex 
side. Even if this case should appear to be extreme there is no 
question that sharp curves are to be avoided in designing the 
steam passages. 

Tests on a de Laval Turbine. — The following are results of 
tests on a de Laval turbine made by Messrs. J. A. McKenna 

* Theory of the Steam Turbine, p. 49. 



486 



STEAM-TURBINES 



and J. W. Regan * and by Messrs. W. W. Ammen and H. A. C. 
Small. t 



Number of nozzles 

Boiler pressure gauge . . . 
Steam chest pressure .... 

Vacuum, inches 

Steam per brake, horse-power 

per hour 

B.T.u. per brake horse-power 

per minute 

Velocity of vanes 

Velocity of jet 

Ratio of velocities 

Efficiency of electric generator 



Regar 


I and McKenna. 


.Ammen and Sti 


6 


6 


6 


6 


6 


153 


" 154 


154.7 


148.8 


148.8 


140 


131-4 


III. 9 


136.9 


78.8 


24-3 


25.2 


25-1 


26 


26 


19.7 


18.0 


20.9 


19-3 


23.2 


355 


326 


379 


350 


426 




1016 




1056 


1037 




3740 




3470 


3770 




0.271 




0-305 


0.275 


0.903 


0.900 


0.864 


0.914 


0.885 



150-7 
140.4 

26.4 

21-5 

374 



0.880 



Compound Steam-Turbines. — There are three ways in which 
impulse-turbines have been compounded (i) the steam may be 
expanded at once to the back-pressure and then allowed to act 
on a succession of moving and stationary vanes, (2) the steam 
may flow through a succession of chambers each of which has 
in it one simple impulse- wheel or (3) a combination of these 
methods may be made, the steam flowing through a succession 
of chambers in each of which it acts on a succession of moving 
and stationary vanes. The first method which gives a very 
compact but an inefficient- wheel, is used for the backing-turbine 
of the Curtis marine-turbine. The second method is used in the 
Rateau turbine, which has usually a large number of chambers. 
The third method is found in the Curtis turbine which has from 
two to seven chambers in each of which are from two to four sets 
of revolving vanes. 

The Parsons turbine, which is an impulse-reaction wheel, has 
a very large number of sets of moving vanes, i.e., from fifty to 
one hundred and fifty. 

The various forms of compound turbines have been devised 
to reduce the speed of the vanes and the revolutions per minute 
to convenient conditions without sacrificing the efficiency. 
* Thesis, M.I.T. 1903. t Thesis, M.I.T. 1905. 



VELOCITY COMPOUNDING 



487 



Velocity Compounding. — In Fig. 107, let V^ represent the 
velocity of a jet of steam that is expanded in a proper nozzle 
down to the back-pressure. 
Suppose it acts on an equal- 
angled (,5 = 7) vane which has 
the velocity V. The relative 
velocity at entrance to that 
vane is V^ and this velocity 
reversed and drawn at V.^ may 
represent the exit velocity, 
neglecting friction. V4 is the 
absolute velocity at exit from 
the vane, which may be re- 
versed by an equal- angled 
stationary guide, and then 
becomes the absolute velocity 
F/ acting on the next vane. 
The diagram of velocities for 
the second moving vane is 
composed of the lines lettered 
F/, F/, F/ and* F/; the 
last of these is reversed by a 
stationary guide, and the 
velocities of the third vane are 
F/', F/', F3" and F/'. The 
diagram is constructed by 
dividing the velocity of whirl 

Vy, = Fj cos ix 

into SIX equal parts, and the final exit velocity F/' is vertical, 
indicating that there is no velocity of whirl at that place. 

It is immediately evident, since the velocity of flow is unaltered 
in Fig. 107, and since there is no exit velocity of whirl that the 
efficiency neglecting friction is the same as for Fig. 103, namely 

e = cos^ a 




as given by equation (291) page 481. 



488 STEAM-TURBINES 

It is, however, interesting to determine the work done on each 
vane; the sum of the works of course leads to the same result. 
In Fig. 107 the velocity of whirl at entrance to the first vane is 

Fj cos a 

and the velocity of whirl at exit is • 

— V4 cos /5 = — 7 Fj <^os a ; 

consequently the work done on the vane is 

- V^ cos a - ( — - V^ cos «) -^1 cos a, 

because V was made equal to one-sixth of the velocity of whirl. 
This expression reduces to 

10 W Tr 2 2 

— ^- F/ cos^ a. 
36 g 

The second and third vanes receive the works 

-— - F/ cos^ a and -- - F/ cos"^ a 
. 3^g 3^ g 



so that the resultant work is 

1 - F/ cos^ a 
g 

and the efficiency is evidently given by the expression already 
quoted. The most instructive feature of this discussion is that 
the relation of the works done on the three vanes is 

5. 3. I- 

A similar investigation will show that the distribution among 
four vanes is 

7. 5> 3. I- 

The first figure in such a series is obtained by adding to the 
number of vanes one less than that number; and each succeeding 
term is two units smaller. Thus seven vanes give the distribu- 
tion 

i3» II. 9) 7> 5. 3. I- 



VELOCITY COMPOUNDING 489 

It is considered that this type of turbine cannot be made to 
give good efficiency in practice on account of large losses in passing 
through a succession of vanes and guides, especially as the steam 
in the earlier stages has high velocities. The turbine, however, 
has certain advantages when used as a backing device for a 
marine-turbine, in that it may be very compact, and can be placed 
in the low-pressure or exhaust chamber, so that it will experience 
but little resistance when running idle during the normal forward 
motion of the ship. 

In dealing with this problem it is convenient to transfer the 
construction to the combined diagram at abij Fig. 107 ; diagrams 
for guides like that made up of the velocities F3, F4 and V^ being 
inverted for that purpose. It is clear that the absolute velocities 
at exit from the nozzle and the guides are represented by Fj,F/ 
and F/', while the relative velocities are V^, V^^ and F/' which 
with no axial thrust are equal to F3, V/ and F3''. The absolute 
velocity at exit from a given guide is taken as equal to the abso- 
lute velocity at exit from the preceding vane, thus F/ is equal 
to F4, etc. The last absolute velocity F/' is equal to at the 
constant velocity of flow. 

The angles a, /?, a^, /?j, a^ and /?2 are properly indicated as may 
be seen by comparing the original with the combined diagram. 

If the diagram is accurately drawn to a large scale, the velocities 
and angles can be measured from it, or they may readily be 
calculated trigonometrically. Thus 

-J sin a ^ sin a ^ 

tan /? = ; tana, =- etc., 

t cos a I cos a 

F2 = V^ sin a cosec j3; F/ = F^ sin a cosec a^, etc. 

The radial length of the vanes and guides must be increased 
inversely proportional to the velocities, using relative velocities 
for the vanes and absolute velocities for the guides. 

There appears to be no reason why the guides should be 
relieved from axial thrust provided they can be properly sup- 
ported. 



490 



STEAM-TURBINES 



Except that the passages in the guides might become too 
long or too sharply curved, they might all be given the same 
delivery angle as the nozzle, and thus a notable improvement 

in economy could be 
realized. In Fig. io8 
the velocities Fj, V^ 
and F4, are drawn in 

the 




Fig. 108. 



the usual manner, 
being equal to V^; 
velocity F4 is laid off 
along the same line as 
Fj and is lettered F/ 
and serves as the initial 
velocity for a new con- 
struction as indicated. F/ is in like manner laid off for F/', 
and thus the diagram is completed. The velocity of the vanes 
of course remains constant with the value F. 

Following the problem on page 444 for a nozzle discharging 
from 150 pounds by the gauge into 26 inches of vacuum we have 
Fj = 3500 feet per second with y = 0.15. The value of F may 
be taken as 620 feet per second, which gives a diagram with no 
final velocity of whirl. 

The exit velocity of whirl from the first set of vanes is — 1830 
feet per second as measured on the diagram, and since the initial 
velocity of whirl is 

Fj cos a = 3500 X 0.866 = 3030 
the retardation is 



3030 - ( - 1830) = 4860. 
The retardation for the second set of vanes is 
2160 — ( — 880) = 3040, 
and for the third set is 1320, so that the work of the impulse is 



w 



(4860 -I- 3040 -f 1320) X 620 — 

o 



w 
1:720000— , 

g 



EFFECT OF FRICTION 491 



and as the intrinsic energy of the jet is 

W y^ ^ - ^w , w 

— Vi = h 3500 - = 6125000- 
2g g g 

the efficiency of this arrangement without losses and friction 

appears to be 

5720 -^ 6125 = 0.92. 

Effect of Friction. — The effect of friction is to change some 
of the kinetic energy into heat, thereby reducing the velocity and 
at the same time drying the steam and increasing the specific 
volume so that the length of the guides and vanes must be 
increased at a somewhat larger ratio than would otherwise be 
required. 

A method of allowing for friction is to redraw the diagram of 
Fig. 107, shortening the lines that represent the velocities to 
allow for friction. 

In order to bring out the method clearly an excessive value 
will be assigned to the coefficient for friction, namely, y = 0.19, 
so that the equation for velocity may have for its typical form 

Vq = V2gh {1 — y) = 0.9 \^2gh. 

Again the coefficient will be assumed to be constant for sake of 
simplicity, more especially as but little is known with regard to 
its real value. 

The diagram shown 
by Fig. 109 was drawn 
by trial with V^ = 3500 
and with a = 30°. It 
appeared necessary to 
reduce V to 380 feet 
per second, instead of 
505 feet, which would 
be proper without fric- 
tion, this latter quantity 

being one-sixth of the fig. 109. 

initial velocity of whirl, 

V^ = Fj cos a = 3500 X 0.866 = 3030. 




492 STEAM-TURBINES 

Starting with V^ the velocity of the jet, the triangle V^, F, V^ 
is drawn to determine the initial relative velocity for the first set 
of vanes. The exit velocity V^ is made equal to 0.9 Fj, and the 
triangle F3, F, F4 is drawn to determine the absolute velocity 
at exit F4 from the guides. This is taken to be the velocity at 
entrance to the guides, but the exit velocity from them is taken to 
be F/ = 0.9 F4. Two repetitions of this process complete the 
diagram. The velocities of whirl at entrance to the three sets of 
vanes as measured on the diagram are 

3030 1780 800, 

and the velocities of whirl at exit from those vanes are 

— 1890 — 880 — o, 

so that the negative accelerations are 

4920 2660 800, 

making a total of 8380. Since the velocity of the vanes is 380 
feet per second the work delivered to the turbine is 

w w 

8380 X 380— = 3180000—, 

g g 

and consequently, using the kinetic energy already computed for 
the jet on the preceding page, the efficiency is 

3180000 -^ 6125000 = 0.52. 

This method preserves the equality of the angles of the vanes 
and guides, but does not avoid axial thrust, for Fig. 109 shows a 
large reduction of the velocity of flow, and as there are no reversals 
of flow, the reduction is a measure of the impulse producing 
axial thrust. Nearly half of the thrust is borne by the fixed 
guides, and it is to be borne in mind that the assumption of an 
exaggerated coefficient for friction greatly exaggerates this 
feature, which in practice may not be very troublesome. 

To entirely avoid axial thrust it appears to be necessary only 
to slightly increase the angle 7 at the exit from the vane; the 
angles of the guides may be reduced if desired as an offset. 



PRESSURE COMPOUNDING 



493 




Fig. iio. 



In Fig. no an attempt is made to avoid axial thrust on 
the vanes, and at the same time to retain a fair efficiency 
by making the 
delivery angle of 
the guides constant. 

A calculation like 
that on page 492 
indicates that an 
efficiency of 0.76 
might be expected 
in this case. It is 
quite likely that 
in practice there 
might be difficulty 

in making the delivery angle of the guide as small as 30°, 
but it appears as though the common idea that it is practically' 
impossible to make an economical turbine on this principle is 
not entirely justified. 

Pressure Compounding. — The second method of compounding 
impulse turbines with a number of chambers each containing 
a single impulse wheel like that of the de Laval turbine requires 
a large number of stages to give satisfactory results. For sake 
of comparison with preceding calculation we will take the 
same initial and final pressure and the same angle for the nozzles, 
namely, 150 pounds by the gauge and 26 inches vacuum, and 
a = 30°. 

Nine stages in this case will give approximately the same 
speed of the vanes as in the problem on page 490. The temper- 
ature-entropy table which was made for work of this nature 
is most conveniently used with temperature, and in this case the 
initial and final temperature can be taken as 366° F. and 126° F. 
At 366° F. the steam is found to be nearly dry for the entropy 
1.56 and that column will be taken for the solution of this 
problem. The heat contents is 1 193.3 instead of 1 193.6 as 
found for 366° F. in Table I of the " Tables of Prop- 
erties of Steam." On the other hand the table gives at 



494 STEAM-TURBINES 

126° for the heat contents 904.9, and the difference is 

1193-3 - 904.9 = 288. 

If we divide the available heat into nine portions we have 
for each 

288 ^ 9 = 32 B.T.U. 

If again we take y = o.i which may be excessive in this case 
since, as will be evident, simple converging nozzles will be 
required, the velocity of the steam jet will be 



F, = \/2 X 32.2 X 778 X 32 X (i - 0.1) = 1200 

feet per second. This is of course the velocity for all the stages. 
The choice of « = 30° gives for the velocity of whirl 

1200 cos 30® == 1200 X 0.866 =- 1040, 

and the velocity of the vanes to give the maximum economy is 
half of this or 520 feet per second or somewhat less if allowance 
be made for friction and other losses. 

Since we have to deal with a single impulse wheel in each 
chamber and since the wheels are usually designed to avoid axial 
thrust, all the conclusions concerning that type of wheel may be 
assumed at once as has already tacitly been done. 

One of the important conclusions is that the efficiency without 
friction as given by equation (291) page 481 is ^ 

e = cos^ a; 

with a = 30°, this gives e = 0.75. 

It is but fair to say that a smaller angle of a is used for this 
type of turbine and that the range of temperature is likely to be 
extended at both limits, and that in particular great importance 
is attached to securing a good vacuum; 28 inches of mercury, 
corresponding to one pound absolute, is commonly obtained 
in good practice with all compound turbines. 

If the peripheral speed of the wheel must be kept down, this 
type of turbine is likely to have a very large number of chambers. 
For example, if the speed must be no more than 260 feet per 
second (half of 520), there must be 36 chambers instead of 9. 



PRESSURE COMPOUNDING 



495 



This will give for the available heat for each chamber 8 
thermal units, and using as before y = o.i we shall have 



F, = V2 X 32.2 X 778 X 8 X 0.9 = 600 

feet per second. With a = 30° the velocity of whirl is now 520 
feet and the velocity of the vanes as stated is 260 feet per second. 

The next question in the discussion of this turbine is the 
distribution of pressure. If the coefficients for friction and 
other losses are taken to be constant, then the pressure can be at 
once determined by the adiabatic method. 

In the problem already discussed 32 b.t.u. are assigned to 
each stage, and if this figure be subtracted nine times in succes- 
sion from the heat contents 11 94 at the initial temperature we 
shall have the values which may be used in determining the 
intermediate temperature and pressure from the temperature- 
entropy table. Also from that table or from Table I in the 
" Tables of Properties of Steam," the corresponding pressures 
can be determined. The work is arranged in the following 
table: 

DISTRIBUTION OF PRESSURE. 





Values of ocv-^-q. 


Temperatures. 


Pressures absolute. 


Ratios of pressures. 





1 193 


366 


165 


0.68 • 


I 


I161 


336 


112 


0.66 


2 


1 1 29 


306 


73-5 


0.65 


3 


1097 


278 


47-8 


0.64 


4 


1065 


251 


30.4 


0.61 


5 


1033 


224 


18.6 


0.61 


6 


lOOI 


199 


II 3 


0.58 


7 


969 


174 


6.55 


0-57 


8 


937 


150 


371 


0-53 


9 


905 


126 


1.98 


0. 



The last column gives the ratio of any given pressure to the 
preceding pressure, i.e. 112 :*i65 = 0.68. These ratios indicate 
that simple conical converging nozzles will be sufficient for all 
but the last stage. With the usual number of stages, twenty or 
more, the ratios are certain to be larger than 0.6 in all cases, 
indicating the use of converging nozzles throughout. 



496 STEAM-TURBINES 

To determine the sizes of the nozzles or the passages in the 
guides it is necessary to estimate the quality of the steam in 
order to find the specific volume. To do this we may consider 
that, of the heat supplied to a certain stage of the turbine, a 
portion is changed into work on the turbine vanes, some part is 
radiated, and the remainder is in the steam that flows from the 
chamber of that stage; if there is appreciable leakage, special 
account must be taken of it, but both radiation and leakage 
can be left at one side for the present. 

Now in the case under consideration, 32 thermal units were 
assigned to each stage in the adiabatic calculation for the 
distribution of pressure. But o.io part was assigned to y to 
allow for friction so that only 0.9 was applied to the calculation 
of velocity; of the kinetic energy of the jet 0.75 only was 
assumed to be applied to moving the vanes without friction, the 
remainder being in the kinetic energy of the flow from the 
vanes which was assumed to be changed into heat again; and 
further there was an allowance of o.i for losses in the vanes, 
leaving a factor, 0.9, to be applied for that action. Conse- 
quently instead of 32 thermal units changed into work per 
stage, our calculation gives only 

32 X 0.9 X 0.75 X 0.9 = 19.44 B.T.U. . 

will be changed into work. A method of determining the quali- 
ties and specific volumes at the several nozzles is illustrated in 
the table on the following page. 

The quantity of heat changed into work per stage is sub- 
tracted successively, giving the apparent remaining heat contents 
as set down in the tables. At a given temperature we may find 
the quality by subtracting the heat of the liquid from the heat 
contents and dividing the remainder by the value of r. The 
specific volumes are determined by the equation 

r ~ %u -\- a^ 

but as X is in all cases large, the effect of <r may be neglected 
altogether. 



PRESSURE COMPOUNDING 



497 



FIRST COMPUTATION OF QUALITIES AND VOLUMES. 





Temper- 
ature 

(0 


Heat 
contents 
(.vr+g) 

II93 


Heat of 
liquid 


Value 
of 

XT 


Heat of 
vapori- 
zation 
(r) 


Quality 
(v) 


Specific volumes 
isx) 


o 


366 


338 


855 


855 


I 


2.78 


2.78 


I 


336 


I174 


307 


867 


878 


0.988 


3 


95 


3 


90 


2 


306 


II54 


276 


878 


899 


0.978 


5 


79 


5 


66 


3 


278 


1135 


247 


888 


919 


0.976 


8 


65 


8 


44 


4 


251 


II15 


220 


895 


939 


0-953 


13 


3 


12 


7 


5 


224 


1096 


192 


904 


958 


0.944 


21 





19 


8 


6 


199 


1076 


167 


909 


975 


0.932 


34 


I 


31 


8 


7 


174 


1057 


142 


915 


993 


0.922 


56 


8 


52 


2 


8 


150 


1037 


118 


919 


lOIO 


0.910 


97 





88 


3 


9 


126 


1018 


94 


924 


1026 


0.901 


175 


158 






By the aid of the temperature-entropy table, the qualities 
and specific volumes may be determined directly v^ith good 
approximation, it being necessary only to follov^ the line of the 
temperature to an entropy column, having nearly the proper 
heat contents. 

There is a serious objection to this method as applied, because 
it does not take any account of the fact that as the steam passes 
from stage to stage losing less heat than it v^ould with adiabatic 
action, the entropy increases, and that with increased entropy 
the difference of heat contents between two given temperatures 
increases. This will be very apparent from inspection of a 
temperature-entropy diagram or the temperature-entropy table. 
This matter will be discussed more at length in connection with 
the Curtis type of turbine. 

It has been assumed that the same amount of heat should be 
assigned to each stage for the adiabatic calculation and that the 
values of y to allow for friction and losses remain constant. 
As to the values that should be assigned to y, we have very little 
published information; it may be noted in passing that our 
allowance for friction in the nozzles and guides is probably too 
large. It will be evident that there is no difficulty in maintaining 
the amount assigned to each stage in its proper proportion even 



498 



STEAM-TURBINES 



though y shall be varied from stage to stage. For example, our 
choice of o.i for both y and y^ gives 

32 X 0.9 X 0.9 = 25.92 B.T.U., 

which multiplied by 0.75, the efficiency due to the angles and 
velocities, gives 19.44 b.t.u. as above. Let it be assumed for 
the moment that the above product shall be kept constant, so as 
to obtain the same velocity of jet in each stage. Then the 
following table exhibits a way of accomplishing this purpose 
while varying y and y^\ 



Stage 


I 


2 


3 


4 


5 


6 


7 


8 


9 


y 

y^ ..... 
(i-y) (i-3'i) 

B.T.U 


0.08 
0.088 
0.839 
309 


0.085 
0.091 
0.832 
31.2 


0.09 
0.094 
0.824 
315 


0.095 
0.097 
0.817 
31-7 


0. 10 
0. 10 
0.81 
32 


0. 105 
0. 103 
0.803 

32-3 


0. II 
0. 106 
. 796 
32.6 


O.I15 
0.109 
0.787 
33-0 


0. 12 
0. 112 
0.781 
33-2 



The last line shows the proper assignment of thermal units 
for this condition. For simplicity both y and y^ are assumed 
to vary uniformly, but other variations can be worked out with 
a little more trouble. Evidently the sum of the figures in the 
last line should be equal to 

9 X 32 -= 288; 

it is a trifle larger in the table. 

Now it is probable that the best values of the factor for friction 
and resistance are to be derived from investigations on turbines 
rather than from separate experiments on nozzles and vanes, 
and it is evident that the use of the methods of representing 
the friction by a factor y is rather a crude way of trying to attain 
in a new design favorable conditions found in a turbine already 
built. 

Since the general conditions of this problem are the same as 
those on page 481, the efficiency due to adiabatic action will be 
the same as is also the efficiency due to the angles and velocities. 
Taking the factors for friction in the guides and blades as each 



PRESSURE COMPOUNDING 499 

O.I, the corresponding factors are 0.9 and 0.9. The efficiency 
due to velocities is 0.75, and the mechanical efficiency may be 
estimated as 0.9. The combined efficiency of t^he turbine is 

0.262 X 0.75 X 0.9 X 0.9 X 0.9 = 0.143. 

A computation like that on page 483 with this efficiency gives 
for the probable steam consumption 16.2 pounds per brake 
horse-power per hour. 

Assume that the turbine is to deliver 500 brake horse-power; 
then the steam consumption per second will be 

16.2 X 500 -^ 3600 = 2.25 pounds. 

We can now determine the principal dimensions of the turbine 
to suit the conditions of its use. Suppose that it is desired to 
restrict the revolutions to 1200 per minute or 20 per second ; 
then with nine stages and a peripheral velocity of 520 for the 
vanes the diameter will be 

520 -^ 207Z = 8.28 feet. 

For a turbine of the power assigned this diameter will be 
found to be inconveniently large. If, however, the number of 
stages can be made 36, the velocity will be reduced to 260 feet 
per second as computed on page 495. This will give for the 
diameter 

260 -i- 207r =4.14 feet. 

The remainder of our calculation will be carried out on these 
assumptions, namely, that the power is to be 500 brake- 
horsc-power, and that there are to be 36 stages. If the method 
of the table on page 497 were applied to a turbine having the 
full 36 stages now contemp ated, it would have 37 lines; namely, 
the ten already set down, and three intermediate entries between 
each pair of consecutive lines; but the temperatures found in 
that table would be found in the more extended table together 
with their specific volumes. We can, therefore, use that table to 
calculate areas and lengths of vanes for 9 out of the 36 stages, 



SOO 



STEAM-TURBINES 




Fig. III. 



which will suffice for illustration. Beginning with the lowest stage 

the area to be supplied will be 

2.25 X 158 -^ 600 = 0.592 square feet; 

where 600 is the velocity of the jet computed on page 495. 

The circumference of a circle having the diameter of 4.14 feet 

is 13 feet; but of this a portion, one-fourth or one-third, must be 

assigned to the thickness of the guides. If we take one-fourth 

in this case the effective perimeter 
becomes 9.75 feet. But as is evi- 
dent from Fig. 11 1 the peripheral 
space assigned to the distance 
between guides must be multiplied 
by sin a in order to find the effec- 
tive opening. As a is taken to be 
30°, the sine is one-half, so that the 
total width of spaces between 
guides is reduced to 4.88 feet. The 

radial length of the guides for the last stage will consequently be 
0.592 -^ 4.88 = 0.123 of a foot = 1.45 inches, 

provided that there is full peripheral admission to the guides. 

Now the angles for this case are the same as those on page 481 
and /9 is 49° 10'. Consequently the relative velocity is 
F2 = Fj sin a -^ sin ^ = 600 sin 30° -=- sin 49° 10' = 397 feet. 

If the passages between the vanes are made of constant width, 
as shown in Fig. iii, the effective perimeter will be the entire 
perimeter of the wheel less the allowance for thickness. An 
allowance like that for the guides will make the vanes shorter 
than the guides in this case. Let us try making the thickness 
equal to a space; then the effective perimeter will be 6.5 feet. If 
the density of the steam is assumed to be constant for a given 
stage, then the lengths of the guides and vanes will be inversely 
as the product of the velocities by the effective perimeters, so 
that the length of the vane will be 
600 X 4."'^ 



1.45 X 



397 X 6.5 



= 1.65 inches. 



LEAKAGE AND RADIATION 



501 



Conversely, if desired, the thickness of the vanes could be 
adjusted to give the same length. Such a construction as this 
leads to is likely to give too sharp a curvature to the backs of 
the vanes, and it may be better to give only the thickness 
demanded for strength and take the chance that the passage 
between the vanes shall not be filled. If allowance is made for 
friction and the consequent reduction in velocity the lengths of 
the vanes should be correspondingly increased. 

The lengths, of the guides for the other stages will be directly 
proportional to the specific volumes in the table on page 497, 
because the velocities have been made the same for all the stages. 
For example, at 199° the length for full admission will be 

1.45 X 31.8 ^ 148 = 0.312 inch, 

which will be the proper length for the twenty-fourth stage. If 
it is considered undesirable to further reduce the length we may 
resort to admitting steam through guides for only a portion of 
the periphery. Making the arc of admission vary as the specific 
volumes, the fourth stage (line i of the table on page 497) will 
have admission for 

360 X 3.86 -^ 31.8 = 43°. 

Intermediate lengths of vanes and arcs of admission may be 
computed by filling out a table like that on page 497 for all the 
stages, or a diagram may be drawn from which the required 
information can be had by interpolation; the values on the line 
numbered o are for this purpose, there being of course no corre- 
sponding stage. In fact the method of computing at convenient 
intervals and interpolating from curves is likely to be more accu- 
rate as well as more convenient, as the error of adiabatic calcula- 
tions for steam with small change of temperature is liable to be 
excessive. 

Leakage and Radiation. — This type of turbine, as will be seen 
in the description of the Rateau turbine, has a number of wheels 
each in its own chamber, and the chambers are separated by 
stationary disks that extend to the shaft. Reduction of leakage 
must be attained by a small clearance between the disk and the 



502 STEAM-TURBINES 

shaft for a proper bearing or stuffing box cannot be placed in so 
inaccessible a place. The leakage can be estimated by aid of 
Rankine's equation on page 432 or from Rateau's experiments 
on page 433 ; but both methods are likely to give results that are 
too large, and a factor less than unity should be applied; but 
the value of such a factor for a long, narrow, annular passage is 
not known, and any estimate must be crude. For a turbine of 
the Rateau type the leakage is likely to be less than five per cent 
at- the high pressure end. Now the leakage is proportional 
nearly to the difference of pressure between successive chambers, 
and as the difference decreases so also does the leakage till it 
becomes of no account at the lower end. To allow for leakage 
the length of guides or the arc of admission may be increased at 
the high pressure end of the turbine. There does not appear 
to be any information concerning the radiation from steam- 
turbines. On the one hand the area of radiating surface is 
larger than for steam-engines and on the other the temperatures 
are less for the greater part if not all of that area. For compact 
steam-engines the radiation is likely to be from five to ten per 
cent. For turbines of the Rateau and Curtis types the effect 
of radiation is to require larger areas in guides and passages 
at the high pressure end. 

Lead. — Turbines with pressure-compounding usually have 
some space between the vanes of one wheel and the next 
set of guides or nozzles, and consequently the absolute exit 
velocity is mainly if not entirely dissipated, so that the steam 
enters those nozzles with no appreciable velocity. If this action 
is complete it would appear to be of little consequence where the 
guides or nozzles are placed. Nevertheless considerable impor- 
tance is attached to locating the guides so that steam from the 
wheel shall flow directly into them. Clearly, as it takes an 
appreciable time to flow through the passages between the 
vanes, the steam will be discharged at some distance from the 
place at which it was received and the general path of the steam 
is a spiral wound around the turbine case in the direction of 
rotation. 



RATEAU TURBINE 



503 



Let abcde represent a vane which has steam entering it 
tangentially with the velocity V^, while it has itself the velocity 
V. Assuming that the relative velocity is 
constant we may divide the curve into a 
number of equal small parts that are approxi- 
mately straight. From b lay off 

bb' 



, V 

ab—, 

^ 2 




Fig. 



then 6' will be a point in the trajectory of the particle of steam. 
In like manner 



cc 



V 

2ab — , etc. 



Casing 



The path ab'c'd'e' may be taken as the trajectory of the steam, and 
e^ is the lead as defined above. Properly a similar construction 
should be made also for the back of the vane, and the mean path 
should be taken to establish the lead. Extreme refinement is 
probably neither necessary nor justifiable in this work. 

Rateau Turbine. — The construction of this turbine, which is 

of the pure pressure-compound 
type is represented by Fig. 113, 
which is a half section through 
the shaft, wheels and casing. 
The wheels are light dished 
plates which are secured to 
hubs that are pressed onto the 
shaft and which carry the 
moving vanes. The chambers 
are separated by diaphragms 
of plate steel, riveted to a rim 
and to a hub casting. The 
hubs are bushed with anti- 
friction metal that is expected 
to wear away if it by chance 
touches the shaft. This tur- 
bine is sometimes divided into 
two sections to provide a middle bearing for the shaft, which 
has considerable length and should preferably have a small 




504 



STEAM-TURBINES 



diameter to reduce leakage. The high pressure portion may 
have a smaller diameter to facilitate arrangement of guides and 
vanes. Sometimes t'here are three diameters for the same pur- 
pose. But little extra complication of computation is introduced 
by such change of diameter; all that is necessary is to make 
the portion of available heat per stage larger in proportion to 
the increase in peripheral speed. 

TESTS ON RATEAU TURBINE. 
Dr. a. Stodola.* 



Duration minutes 

Revolutions per minute 

Steam pressure at stop valve absolute 
pounds 

Superheating degrees F 

Steam pressure at first guides .... 

Superheating degrees F 

Absolute exhaust pressure 

Effective power 

Steam per horse-power per hour, ex- 
clusion of air-pump . 



40 


50 


35 


180 


2184 


2181 


2190 


2101 


176. 1 


I75-I 


170-5 


168.4 


5-2 


9 


14.8 


20 


44-7 


639 


95-4 


119. 9 


32.6 


32.2 


20.9 


18.9 


1.29 


^■33 


I-5I 


1 .64 


172 


257 


417 


531 


19.0 


17.6 


15-7 


156 



30 

2200 

181. 1 

14.6 

143-7 
17. 1 
1.89 
634 

152 



The accompanying table gives . results of tests on a Rateau 
turbine by Professor Stodola. To compare with results from 
steam-engines, these latter should be referred to brake horse- 
power, with a mechanical efficiency of 0.85 to 0.90. 

This type of turbine has been applied successfully to use 
exhaust steam from reciprocating engines which for some purpose 
exhaust at atmospheric pressure or into a poor vacuum. Such 
application can, however, be but local or accidental. 

Steam Friction of Rotating Disks. — The resistance which a 
turbine wheel experiences while rotating in steam can be divided 
into two parts : first, that due to the friction of the smooth disk, 
and second, that due to the action of the vanes, which have an 
effect comparable to that of a centrifugal pump. 

From a consideration of tests made by Odell f on cardboard 
disks, and by Lewecki J on a de Laval turbine wheel driven in 

* Steam Turbines, trans. Dr. L. C. Lowenstein. 

t Engineering, January, 1904. t Zeitschr. d, V. deutsch Ing., 1903. 



SIDE THRUST 505 

its casing, and from tests of his own, Professor Stodola gives the 
following equations for the horse-power required to drive smooth 
wheels and to drive wheels with vanes forward: 
Smooth wheels 

H.P. =0.02295 a^ D'-' (— ) 7. 

Wheels with vanes 

H.P. = [0.02295 «i^'*' + 1.4346 ^2 L'-''] (—)\ 

Vioo / 

where D is the diameter in feet, L is the blade length in inches, 
V is the peripheral speed in feet per second, and 7 is the density 
of the medium. The values of the other factors are 

«i = 3-14 «2 = 0-42. 

These formulae explain why the backing turbine for marine 
propulsion is always run in a vacuum when idle. 

Turbines which have only a partial admission must be affected 
by some such action for that part of the revolution during which 
steam is not admitted; but this matter is obscure and such a 
resistance must be combined with friction and other resistances. 
It is therefore very difficult to assign the proper value to the fric- 
tion factor y for steam in the vanes or in the guides and vanes of 
a velocity-compound turbine. In particular any change of the 
angle 7 (Fig. 103, page 480) to avoid end thrust must be made 
with caution and should be checked by experiment. 

Side Thrust. — If admission is restricted to only a part of the 
periphery of a turbine, then in order to preserve a balance and 
avoid unnecessary pressure ^on the bearings of the shaft, the arc 
of admission should be divided into two equal portions, that are 
diametrically opposite. Some builders, however, prefer to 
ignore this effect, and concentrate the admission at one side, 
because there is tendency for the steam to spread which will have 
double the effect if the arc is divided as suggested. The amount 
of side thrust can be estimated from the powers developed at 
the several wheels, having partial admission, together with the 
dimensions and speed of revolutions, making allowance of course 
for the distribution of the torque over an arc of a circle. 



5g6 steam-turbines 

Pressure and Velocity Compounding. — A favorable combina- 
tion may be made of the two methods of compounding already 
discussed; that is, the pressure and temperature range may be 
divided between two or more chambers in each of which shall be 
two or three sets of moving vanes. This has been done on a 
large scale with the Curtis turbine which appears to have a wider 
range of economical application than any other type. 

Since the principles of each method have been discussed 
already, we will illustrate the application to a comparatively 
simple problem avoiding too great minutiae of detail. 

Let us take for the principle conditions the delivery of 500 kilo- 
watts of electrical energy, which, with an efficiency of the dynamo 
of about 0.9, will correspond to nearly 770 brake horse-power. 

Let the initial pressure be 150 pounds by the gauge, and the 
vacuum be 28 inches of mercury. Let the angle of the nozzles 
be rt = 20°. The absolute pressures will be about 165 pounds 
and one pound absolute, and the compounding temperatures 
are 366° and 102° F. Dry saturated steam at the given pressure 
will have nearly 1.56 units of entropy, and for this the temperature- 
entropy table gives for adiabatic expansion with the above limits 
of temperature the heat contents as 1193 ^^^ ^7^- ^^^^ value 
of ^2 is 70 at the lower temperature, and consequently x^^ 
is equal to 801 b.t.u. 

The thermal efficiency of adiabatic expansion without allowing 
for any losses is 

XJr^ 801 o 

6=1 — ^~^ =1 = 0.285; 

^ + ^i - ^2 II23 

the corresponding heat consumption is 

42.42 H- 0.285 "^ 145 B.T.U. 

per horse-power per minute. 

The efficiency for the turbine without friction by equation 
(291), page 481 is 

e = cos^ a = 0.883. 

The efficiency of the nozzles has already been determined to be 
0.85 by the selection of 0.15 for y. Let us further assume that 



PRESSURE AND VELOCITY COMPOUNDING 507 

the combined effect of losses in the vanes may be taken to be 
equivalent to making y^ equal to 25 so that i — >'(j is 0.75; this 
is in effect the efficiency factor for the vanes as affected by friction. 
If, further, we take the mechanical efficiency of the machine as 
0.9, then the combined efficiency for the turbine will be 

0.285 X 0.883 X 0-85 X 0.75 X 0.9 = 0.144. 

This corresponds to 

42.42 ~ 0.144 =^ 295 B.T.U. 

per horse-power per minute. Now it costs to make steam from 
water at 102°, and at an absolute pressure of 165 pounds, 11 23 
(r^ + 5^1 — ^2) thermal units, as already calculated in the deduc- 
tion of the efficiency of adiabatic action. Consequently the steam 
per horse-power per hour will be 

295 X 60 ^ 1123 - 15.7 

pounds per brake horse-power per hour. To this should properly 
be added a fraction, to allow for leakage and radiation, amounting 
to five or ten per cent; this added amount of steam will affect 
the size of the high pressure nozzles only in this case, and as 
extra nozzles are sure to be provided we will take no further 
account of it than to say that the steam consumption may amount 
to 16.5 to 17.3 pounds per brake horse-power per hour. 

The heat contents which have already been found give for the 
adiabatic available heat 

1193 - 871 - 322, 

and if this be divided equally we have 161 thermal units per 
stage. Using 0.15 for y in the nozzles, the velocity of the jet 
becomes 

V =^2 X 32.2 X 778 X 161 X0.85 =2610 

feet per second. 

Assuming that we may use three sets of moving vanes the 
velocity for them will be 

2610 -- (2 X 3) = 435 
feet per second. 



5o8 STEAM-TURBINES 

If we choose a diameter of 4^ feet for the pitch surface of the 
vanes it will lead to the use of 1850 revolutions per minute. 

To find the intermediate pressure we may take for the heat 
contents at that pressure 

1193 - 161 = 1032, 

which in the temperature-entropy table corresponds to 223° F., 
or 18.2 pounds. Since the back- pressure for the nozzles is rela- 
tively small in each case, the nozzles will have throats for which 
the velocities must be determined in order to find the areas. 
The throat pressures may be taken to be 

165 X 0.58 = 95.6; 18.2 X 0.58 = 10.6, 

and the corresponding temperatures are 324° and 196° F. 

Since the rounding of the nozzle is likely to give but small 
area for friction compared with the cone for expanding to the 
back-pressure, we may assume adiabatic expansion to the throat 
and allow the entire value of >' = 0.15 for the computation for 
the exit. This appears to agree with tests showing that such 
nozzles give nearly full theoretical discharge. The heat contents 
by the temperature-entropy table at entropy 156 and 324° F. 
amounts to 1149 b.t.u., the value of x is 0.964 and the specific 
volume is 4.45 cubic feet. The apparent available heat is 

1193 - 1149 = 44B.T.U., 

giving a throat velocity of 



V ^ V2 X 32.2 X 778 X 44 = 1480. 

The. apparent available heat for producing velocity at the exit 
with y taken at 0.15 is 

0.85 X 161 = 137 B.T.U., 

leaving for the available heat 

1 193 - 137 = 1056 B.T.U. 
The heat of the liquid is 191 so that with 959 for r we have 
x' = xV ^ r' = (1056 — 191) -^- 959 -= 0.902. 



PRESSURE AND VELOCITY COMPOUNDING 509 

The specific volume is 

v= (xu -\- a) = 0.902 (21.6 — 0.016) + 0.016 = 19.5. 

With 15.7 pounds of steam per brake horse-power per hour 
and 770 horse-power the steam per second is 

w = 15.7 X 770 -^ 3600 = 3.36 pounds. 

The combined area of discharge of all the first stage nozzles 
is therefore, with the velocity at exit equal to 2610 feet, 

3.36 X 19.5 X 144 -^ 2610 = 3.62 square inches. 

The nozzles of turbines of this type are sometimes made square 
at the exit so as to give a continuous sheet of steam to act on the 
vanes. If the side of such a nozzle were made half an inch 
there would appear to be fourteen and a half such nozzles; the 
turbines would probably be given 16 or 18 of them, which could 
be arranged in two groups. Since the angle of the nozzle is 20° 
the width of the jet measured along the perimeter of the wheel 
will be 

0.5 ^ sin 20° = 0.5 -^ 0.3420 = 1.46 inch. 

Allowing one-fourth of the width of the orifice for the thickness 
of the walls, the width occupied by eight nozzles would be 

1.46 X 1.25 X 8 = 14J inches. 

The combined throat area of all the nozzles will be 

3.36 X 4.45 X 144 -^ 1480 = 1. 41 square inch. 

Dividing by 14I, the number of necessary nozzles, gives for 
the throat area of one nozzle 

1. 41 -^ 14.5 = 0.0972 square inch, 

so that the diameter will be about 0.35 of an inch. 

A method of calculation for the second set of nozzles consistent 
with the method of determining the intermediate pressure is as 
follows: The pressure in the throat has already been found to 
be 10.6 pounds, corresponding to 196° F., for which the tem- 
perature-entropy table at 1.56 units of entropy gives for heat 



5IO 



STEAM-TURBINES 



contents 998. The heat contents at 18.2 pounds (223) has 
already been found to be 1032, so that the available heat for 
adiabatic flow appears to be 34 B;T.u., which gives for the 
velocitv in the throat 



V = \^2 X 32.2 X 778 X 34 = 1300 feet. 

The next step is the determination of the qualities at the throat 
and exit, and from them the specific volumes. Now of the 
161 B.T.u. available for adiabatic flow in the first nozzles only 
a part has actually been changed into work, because there was 
allowed 0.15 for friction in the nozzle, and 0.25 for losses in the 
guides and vanes, while the efficiency due to angles and velocities 
was 0.883. The heat changed into work was therefore 

161 X 0.85 X 0.75 X 0.883 = 90-6 B.T.u. 

Consequently the heat left in the steam as it approaches the 
second nozzle is 

1193 — 91 = 1102 B.T.u. 

per pound. Now r has the value 959 at 223 F., and q is 191, so 
that the quality is 

X = (1102 - 191) ^ 959 = 0.950. 

If the flow from the entrance to the throat 34 b.t.u. are 
assumed to be changed into kinetic energy leaving for 

xr + q = 11*02 — 34 = 1068, 

and as r is equal to 978 and q is 164 at 196° F., we have 

X = (1068 — 164) -^ 978 = 0.925 

at the throat of the second nozzle. 

Allowing as before 0.15 for the friction of the nozzle there will 
be 

0.85 X 161 = 137 B.T.u. 

changed into kinetic energy for the entire nozzle leaving 

xr -\- q = 1 102 — 137 = 965 B.T.u.; 
and at i pound or 102° F., the values of r and q are 1043 and 70 
X = (965 - 70) -V- 1043 = 0,858 



PRESSURE AND VELOCITY COMPOUNDING 511 

at exit from the second set of nozzles. The volume of saturated 
steam at 102° is 335 cubic feet, and with x equal to 0.858 the 
specific volume is 288 cubic feet. Consequently, with a weight of 
3.36 pounds per second, and a velocity of 2610 feet, the united 
areas of all the nozzles at exit will be 

3.36 X 288 X 144 ^ 2610 = 55.6 square inches. 

Now the perimeter of a circle having a diameter of 4J feet is 
about 170 inches. Allowing for the sine of the angle 20° and 
one-fifth for thickness of guides there will be about 43.5 inches 
for the united width of passages between guides so that the 
radial length will be 

55-6 -^ 43-5 = 1-27 inch. 

The specific volume of saturated steam at 197° is 36.2 cubic 
feet, so that with x equal to 0.925 the specific volume is 33.5. 
Now the areas are proportional to the specific volumes and 
inversely as the velocities, consequently the length of guides at the 
throat is 

1.28 X ^-^^ X ^^ = 0.30 inch. 
1300 285 

The length of the vanes and guides can be found by the method 
on page 500, using relative velocities for the vanes and absolute 
velocities for the guides. The velocities decrease as indicated 
by Fig. 107, page 487, and the lengths must be correspondingly 
increased. In this case, however, there are two considerations 
which influences the lengths that should be finally assigned to the 
guides and vanes, (i) The thickness may be diminished, which 
tends to decrease the length. (2) Friction reduces the velocity 
which tends to increase the length. Friction of course diminishes 
all velocities including the peripheral velocity of the wheel, but a 
proper discussion of that matter would be both long and uncertain. 

Attention has already been called to the defect of this method 
of making all the calculations at a single value of entropy and 
trying to allow for friction and other losses by simple factors. 
The difficulty is aggravated in this case by the fact that the 



512 



STEAM-TURBINES 



second set of nozzles or guides have proper throats. The proper 
method after having selected a set of intermediate pressures 
appears to be to calculate the turbine step by step. The steam 
supplied to the second set of nozzles (or guides) has been found 
to have the quality 0.950, and this is probably a good approxima- 
tion to the actual condition, even if allowance is made for radi- 
ation and leakage. The temperature-entropy table gives for 
steam having that quality and the temperature 223, the 
entropy as nearly 1.66. At that entropy the heat contents at 
the initial, throat and exit pressures, are given in the following 
table with also the quality and specific volume at the throat; 
the table also gives the quality and specific volumes at exit with 
y equal to 0.15. 



Pressure. 


Tempterature. 


Heat contents. 


Quality. 


Specific volume. 


18.2 

10.6 

I .0 


223 
196 
102 


1 100 

1063 

927 


0.92 
0.85 


3 33 
28.5 



The apparent available heat for adiabatic flow to the throat 
is now 

iioi - 1063 = 37, 

which would give a velocity of 

F = V2 X 32.2 X 778 X 37 =- 1360, 

instead of 1280 as previously found. The apparent available 
heat to the exit with 0.15 for the friction factor is now 

(iioi - 927)0.85 = 147, 

which gives for the exit velocity 



V = V2X32T2X 778 X 147 = 2710, 

instead of 2610 previously computed. 

This comparison shows that the intermediate pressure deter- 
mined by the customary method will be too high, and that to 
obtain the desired distribution of temperature the factors for 



CURTIS TURBINE 



513 



the lower stages must be modified arbitrarily as may be deter- 
mined by comparison with practice. 

Curtis Turbine. — Fig. 114 shows a partial elevation and section 
of the essential features of a Curtis turbine, which has four 
chambers and two sets of moving vanes in each chamber. The 
axis of the turbine is vertical which demands an end bearing, 
the difficulties of which construction appear to have been met by 




Fig. 114. 

pumping oil under pressure into the bearing, so that there is 
complete lubrication without contact of metal on metal. The 
condenser is placed directly under the turbine, and the electric- 
generator is above on a continuation of the shaft. The arrange- 
ment appears to be convenient, and in particular to demand 
small floor space only. 

When used for marine propulsion the Curtis turbine has a 
horizontal shaft from necessity, and has a large number of stages. 



514 



STEAM-TURBINES 



A turbine developing 8000 horse-power has seven pressure 
stages, each of which but the first has three velocity stages, that 
one has four velocity stages. The diameter is ten feet and 
the peripheral velocity is 180 feet per second. 

Tests on Curtis Turbines. — The following tables give tests 
on two Curtis turbines, having two and four pressure stages, 
respectively; both were made by students at the Massachusetts 
Institute of Technology. 

TESTS ON A TWO-STAGE CURTIS TURBINE. ' 

Darling and Cooper.* 



Duration minutes 

Throttle pressure gauge .... 

Throttle temperature F 

Barometer inches 

Exhaust pressure absolute pounds 

Load kilowatts 

Steam per kilowatt hour, pounds 
Thermal units kilowatt minute . 



120 


120 


120 


120 


146.3 


145-3 


143-2 


143-9 


512 


520 


464 


502 


29.8 


29.9 


29.9 


29.9 


0.82 


0.79 


0.92 


0.84 


161 .4 


255-7 


374.0 


512.9 


21.98 


19.63 


19.98 


18.43 


440 


396 


392 


369 



60 

149-3 
512 

30.0 
0.85 
731-9 

17-75 
357 



If the efficiency of the dynamo is taken at 0.9 and one kilowatt 
is rated as 1.34 horse-power, the steam and heat consumptions 
per brake horse-power are, for the best result, 

1 1.8 pounds 239 B.T.u. 

TESTS ON A FOUR-STAGE CURTIS TURBINE 

COE AND TRASK.f 



Duration minutes 

Boiler pressure, pounds 

Vacuum inches 

Load kilowatts 

Steam per kilowatt hour pounds 
Thermal units per kilowatt (minute) 



60 


60 


60 


180 


152 


149.6 


152-1 


150 


28.5 


28.2 


28.8 


28.4 


282 


380 


523 


562 


21.4 


20.3 


18.8 


19-5 


394 


370 


352 


360 



120 

150.4 

28.3 
788 
19-3 

357 



* Thesis, M. I. T., 1905. 
t Thesis, M. I. T., 1906. 



REACTION TURBINES 



515 



m 



Taking the efficiency of the dynamo as 0.9 and a kilowatt as 
1.34 horse-power, the best result is equivalent to a steam con- 
sumption of 12.6 pounds and a heat consumption of 237 thermal 
units. 

Reaction Turbines. — The essential feature of a reaction 
turbine is a fall of pressure and a consequent increase of veloc- 
ity in the passages among the vanes of the turbine. Since 
such wheels commonly are affected by impulse also they are 
sometimes called impulse-reaction wheels, but if properly under- 
stood the shorter name need not lead to confusion. In conse- 
quence of the feature named the 
relative exit velocity V^ is greater 
than Fj. Another consequence is 
that steam leaks part the ends 
of the vanes which are usually 
open, and there is also leakage 
past the inner ends of the guides 
which are also open; this feature 
is shown by Fig. 115. 

The reaction turbine is always 
made compound with a large 
number of stages, one set of guides 
and the following set of vanes 
being counted as a stage. In 
consequence the exit pressure either 
from the guides or the vanes is 

only a little less than the entrance pressure, and the passages 
are all converging. 

There is no attempt to avoid axial thrust, and therefore the 
exit angle 7 from the vanes may be made small; it is commonly 
equal to the exit angle a from the guides. A common value 
for these angles is 20°. 

The guides and vanes follow alternately in close succession 
leaving only the necessary clearance; the kinetic energy due to 
the absolute exit velocity from a given set of vanes is not lost but 
is available in the next set of guides. The turbines are usually 




Fig. 115. 



5i6 STEAM-TURBINES 

made in two or three sections as shown by Fig. 117, page 526, 
and it is only at the end of a section that the kinetic energy due 
to the absolute exit velocity is rejected; at the end of a section 
this kinetic energy is changed into heat and is in a manner 
available for the next section; at the end of the turbine it is of 
course wasted. Since there are usually sixty stages or more 
the influence of the kinetic energy rejected is likely to be less 
than five per cent and it may properly be combined with the 
general factor to allow for friction and leakage past the ends of 
the guides and vanes. Both influences reduce the change 
of heat into work applied to the turbine and increase the 
value of the quality x and also of the specific volume of the 
mixture of steam and moisture. 

Since the exit absolute velocity from the vanes is applied to 
driving the steam into the next set of guides, there is no direct 
advantage in avoiding velocity of whirl at this place; it is only 
necessary to give the guides the proper angle at entrance to 
receive the steam. Indirectly it is disadvantageous to have a 
high velocity at the entrance to the guides, or, for that matter, in 
any part of the turbine, as the friction is probably proportional 
to the square of the velocity as has been assumed in the use of 
the friction factor y. 

The steam enters a set of guides with a certain velocity, i.e., 
the exit absolute velocity from the preceding set of vanes. 
On account of the loss of pressure in the guides a certain amount 
of heat is .changed into kinetic energy and the equivalent increase 
of velocity may be added to the entrance velocity to find the 
exit velocity which is of course an absolute velocity. This abso- 
lute velocity combined with the velocity of the guides gives the 
relative entrance velocity to the vanes. To this entrance veloc- 
ity is to be added the gain in velocity due to change of heat into 
kinetic energy in the vanes, in order to find the relative exit 
velocity. The ratio of the heat used in the vanes to that used 
in the entire stage is called the degree of reaction. Commonly 
the degree of reaction is one-half; that is, the amount of heat 
used in the vanes is equal to that used in the guides; and 



CHOICE OF CONDITIONS 



517 



the gain of velocity in the vanes is equal to the gain in the 
guides. 

In Fig. 116 let V^ be the velocity of the steam leaving the 
guides and V the velocity of the vanes; then V^ is the relative 
velocity of the steam entering the vanes. V^ is the relative exit 
velocity which is greater than V^ on account of the change of 
heat into work. F4 is the absolute exit velocity from the vanes 
with which the steam enters the next set of guides. If the con- 
ditions for successive stages are the same, F4 is also equal to the 
entrance velocity to the set of guides of the stage under discussion, 
and if ce is laid off at ac' then c'b is the gain of velocity in the 




Fir.. 116. 



guides. Consequently to construct F3 we may lay off c^' equal 
to ac and e'd equal to c'b. Now a and 7 are commonly made equal, 
and therefore the triangles abc and cde are equal. Consequently 
the angle 5 for the entrance to the guides is equal to /? at the 
entrance to the vanes. In fact the guides and vanes have the 
same form. 

Choice of Conditions. — The foregoing discussion shows that 
the designer is given a wider latitude in his choice of conditions 
for the compound reaction turbines than appeared possible 
for impulse turbines, though if the restriction of no axial thrust 
were removed from the latter the comparison would be quite 
different. 



5^8 



STEAM-TURBINES 



The most authoritative statement of the preferable conditions 
in practice for reaction turbines of the Parson's type is formed 
in a paper by Mr. E. M. Speakman,* but much of the infor- 
mation in the hands of the builders " being based on long and 
costly experiments, much reticence is observed regarding their 
publication." The statement of practical conditions is therefore 
based on such information as can be gleaned from his paper, 
with obvious applications by ordinary methods. Factors for 
friction and leakage are largely conjectural, as must in fact be 
the case at present for all turbines, and for our purpose may 
perhaps be limited to giving the student an idea of the nature of 
the problems. 

The ratio of the velocity of the vanes to the velocity of the 
steam has varied in turbines built by the Parsons Company 
from 0.25 to 0.85. In general the ratio may be taken as 0.6. 

These turbines are usually built with two or three diameters 
of the revolving cylinder or rotor as shown in Fig. 117. The 
following tables give the practice of that company with regard 
to peripheral speed and number of stages. 

PARSONS TURBINES — ELECTRICAL WORK. 





Peripheral speec 


, feet per second. 






Normal output 






Number of 
stages. 


Revohitions 


kilowatts. 






per minute. 




First expansion. 


Last expansion. 






5000 


135 


33° 


70 


750 


3500 


138 


280 


75 


1200 


2500 


125 


300 


84 


1360 


1500 


125 


360 


72 


1500 


1000 


125 


'250 


80 


1800 


750 


125 


260 


77 


2000 


500 


120 


285 


60 


3000 


250 


100 


210 


72 


3000 


75 


100 


200 


48 


4000 



Trans. Inst. Eng. and Shipbldn., Scot., vol. xlxix, 1905-06. 



CHOICE OF CONDITIONS 



19 



PARSONS TURBINE — MARINE WORK. 



Type of vessel. 



High speed mail steamers . 
Intermediate mail steamers 

Channel steamers 

Battleships and large cruisers 

Small cruisers 

Torpedo crafts 



Peripheral speed, feet 
per second. 


H.P. 


LP. 


70-80 


I 10-130 


80-90 


110-135 


90-105 


120-150 


85-100 


115-135 


105-120 


130-160 


1 10-130 


160-210 



Ratio of 

velocities, 

vanes to 

steam. 



0.45-0 
0.47-0 
0.37-0 
o . 48-0 

0.47-0 
0.47-0 



Number 

of 

shafts. 



4 

3 
4 

3-4 
3-4 



The Westinghouse Company have used much higher veloc- 
ities of vanes for electrical work than given in the above tables ; 
as much as 170 feet per second for the smallest cylinder and 
375 for the largest cylinder. 

The blade height should be at least three per cent of the 
diameter of the cylinder in order to avoid excessive leakage 
over the tips. Mr. Speakman says that leakage over the tips 
of the blades is perhaps not so detrimental on account of actual 
loss by leakage as because it upsets calculations regarding 
passages by increasing the steam volume. 

The following equation represents Mr, Speakman's diagram 
for clearances over tips of vanes, 



clearance in 
inches 



o.oi + 0.008 diam. in feet. 



The proportions of blades may be taken from the following 

table: 

PROPORTIONS OF BLADES— INCHES. 



Height 1 

Width ^ 

Pitch i| 

Axial clearance ^ 



Mr. Parsons * gives for the efficiency of the steam in the 
turbine blades themselves 0.70 to 0.80. 

* Jnst. Naval Arch., 1903. 



2 


3 


4 


6 


8 


ID 


12 


M 


18 


21 


24 


.30 


-i 




\ 


h 


f 


* 


i 


i 


I 


I 


I* 


li 


1* 


li 


a 


I'i 


2* 


2i 


^ 


2^ 


,ii 


^\ 


^% 


4 


A 


i 


tV 


-i 


tV 


h 


\ 


^ 


h 


f 


W 


i 



520 



STEAM-TURBINES 



In addition to the leakage past the tips of the blades which 
cannot in practice be separated in its effects from friction, 
there is likely to be a considerable leakage past the balance 
pistons which will be described in connection with Fig. 117. 
This leakage is in the end direct to the condenser, and no account 
need be taken of it in the design of the blading of the turbine; 
but allowance should be made in comparing theoretical calcula- 
tions with results of tests. 

Design for a Reaction Turbine. — Let us take for the principal 
conditions the delivery of 500 kilowatts of electrical energy, which 
with an efficiency of the dynamo of about 0.9 will correspond 
to 770 brake horse-power, as for the calculation on page 506. Let 
the initial pressure be 150 pounds by the gauge, and the vacuum 
be 28 inches. The absolute pressures corresponding are 165 
pounds and one pound, and the temperatures are 365°.9 and 
102° F. The calculation referred to gives for the thermal 
efficiency of adiabatic action 0.285, which corresponds to 
145 B.T.u. per horse-power per minute. If we allow 0.60 for 
the turbine efficiency, and ten per cent for leakage to the con- 
denser and radiation, and take 0.9 for the mechanical efficiency 
we shall have for the combined efficiency of the turbine 

0.285 X 0.60 X 0.9 X 0.9 = 0.139. 

This will give for the heat and steam consumption per horse- 
power, 16.3 pounds per hour and 305 b.t.u. per minute. These 
are to be compared with results of tests to determine whether 
the constants assumed are proper. 

For the estimate of the weight of steam to be used in deter- 
mining the dimensions of the turbine we should omit the factor 
for leakage to condenser and radiation, which will give for the 
steam per horse-power per hour 14.7 pounds. The weight of 
steam per second to be used in computing passage therefore 
becomes 

w = 14.7 X 770 -^ 3600 = 3.15 pounds. 

Let the peripheral speed of the smallest cylinder be taken as 
225 feet per second, and let the intermediate and low-pressure 



DESIGN FOR A REACTION TURBINE 521 

cylinders be i J and 2 J times the diameter of the small cylinders. 
Let the peripheral speed be 0.75 of the steam velocity, then the 
latter will be 300 feet per second. If the exit angles for guides 
and vanes be taken as 20° and if the degree of reaction is 0.5, 
the velocities and angles will be represented by Fig. 116, page 
517. In that figure 

gb = Fj cos 20° = 0.940 V^ ; 

and as V is 0.75 V^, 

we have gc = (0.940 - 0.75) V^ = 0.190 V^. 

But ag = Fj sin 20° = 0.342 F^; 

and tan /? = 0.342 -^ 0.190 = 1.800 .•. /? = 61°. 

The angle /? is given to the backs of the blades, and the angle at 
the faces is somewhat larger, as will appear by Fig. 115, page 516; 
in consequence there is some impulse at the entrance to the vanes. 
To get the relative velocity we have 



^2 = ^S + ^^ = (0-342 + 0.190 ) F^' 
.-. F, = 0.392 Fj. 

But it is shown on page 518 that for the conditions chosen the 
increase of velocity in either guides or vanes is equal to 

Fj - F2 = (i - 0.392) F^ = 0.608 X 300 = 182 

feet per second. 

Now the equation for velocity when h thermal units are avail- 
able is 



F = V2 X 32.2 X 778/^, 
and conversely 

h = 182' ^ (64-4 X 778) = 0.661 B.T.U. 

This is the amount with allowance for friction and leakage 
past the ends of the blades which has been assigned the factor 
0.6, so that for the preliminary adiabatic computation we may 
take for one set of blades 

0.661 ^ 0.6 = I.I B.T.U. , 



522 STEAM-TURBINES 

and for a stage, consisting of a set of guides and vanes, we may 
take for the basis of the determination of the proper number of 
stages 2.2 B.T.u. per pound of steam used. 

It appears on page 508 that adiabatic expansion from 165 
pounds absolute to one pound absolute gives 322 thermal units 
for the available heat. If this is to be distributed to the stages 
of a turbine with 2.2 units per stage, then the total number of 
stages will be 

322 -7- 2.2 = 146 

stages. This is under the assumption that the turbine has a 
uniform diameter of rotor with 225 feet for the velocity of the 
vanes; we have, however, taken the intermediate diameter ij 
times the high-pressure and the low-pressure 2 J times. The 
peripheral velocities will have the same ratios, and the amounts 
of available heat per stage will be proportional to the squares of 
those ratios, namely, 2.25 and 6.25. Consequently the amounts 
of heat assigned per stage will be as follows : 

High-pressure Intermediate Low-pressure. 

2.2 4.95 13.75 

If we decide to use ten low-pressures and twenty intermediate 
stages they will require 

10 X 13.75 + 20 X 4.95 = 236.5 B.T.U., 

leaving 84.5 thermal units which will require somewhat more 
than 38 stages. Reversing the operation it appears that one 
distribution calls for 

10 X 13.75 + 20 X 4-95 + 38 X 2.2 - 320 B.T.u. 

For convenience of manufacture it is customary to make 
several stages identical, that is, with the same length of blades, 
clearances, etc.; this of course will derange the velocities to some 
extent and interfere with the realization of the best economy. 
That part of the cylinder which has the same length of blades 
is known technically as a barrel. Let there be three barrels for 
each cylinder, making nine in all, which may be conveniently 
numbered, beginning at the high-pressure end and may have 



DESIGN FOR A REACTION TURBINE 



523 



the number of stages assigned above. In that table is given also 
the number of the stage counting from the high-pressure end, 
which is at or near the middle of the length of the barrel, for 
which calculations will be made. The values of the heat con- 
tents xr + q are readily found for each stage given in the table 
by subtracting the amounts of heat changed into kinetic energy, 
down to that stage, allowing 2.2 for each stage of the high- 

COMPOUND REACTION TURBINE. 















fli 


•§ 


•a 


§ 












m 








% 


^ 


•3 


ft 






8 






1 




3 




42 

u 


4) « 


1 


1 




Specific 
volumes. 


3 


1 


1 


1 

E 

3 


1 

.•2 


1 

a, 

H 


g 




o«< 

32 


"o 

i 


1 


a 




u 


I — 


14 


S 


/ 


P 


xr+Q 


x'r+q 


Q 


r 


x' 


S V 




I— 


7 


350 


135 


1178.6 


ii8s 


321 


867 


0.985 


3.32 


3-27 


0.415 




2 — 


12 


20 


323.5 


93.5 


1150.0 


1168 


294 


887 





985 


4.65 


4.57 


0.578 




3— 


12 


32 


300 


67.2 


1123.6 


1152 


270 


904 





976 


6.39 


6.22 


0.787 


II— 


4— 


8 


42 


271 


42.6 


1090.6 


1132 


240 


924 





965 


9-79 


9.43 


0.532 




5— 


6 


49 


241 


25.4 


1056.0 


IIIO 


210 


945 





954 


15.9 


15.2 


0.854 




6— 


6 


55 


217.5 


16.4 


1026. 3 


1093 


186 


962 





940 


24.1 


22.7 


1.252 


ni— 


7— 


4 


60 


184 


8.19 


983.9 


1068 


153 


986 





929 


46.2 


42.7 


0.867 




8— 


3 


64 


147 


3.44 


935.8 


1039 


IIS 


1012 





913 


104 • 


94.4 


1.92 




9— 


3 


67 


117 


1-55 


894.5 


1014 


85 


1033 


0.901 


221 


199 


4.04 



pressure cylinder, 4.95 for each intermediate stage and 13.75 ^^^ 
each low-pressure stage. For example, the forty-ninth stage has 
its heat contents found by subtracting from the initial heat con- 
tents 1 1 93, the amount 

38 X 2.2 + II X 4-95 = 138, 

leaving for the heat contents after that stage 1055 thermal units. 
The probable heat contents allowing for friction and leakage is 
found by subtracting the product of the above quantity by the 
factor 0.6. Giving 

1 193 — 138 X 0.6 = 1111 B.T.U. 

Having the values oi odr ■\- q obtained in this way, the values of 
xf can be found by subtracting the heat of the liquid q^ and 



524 STEAM-TURBINES 

dividing the remainder by r. Finally the specific volumes are 
computed by the equation 

V = x'w + t; 

but in practice cr may be neglected giving 

u = x's 

because we have either x nearly equal to unity or else s will be 
larger compared with cr. 

The steam velocity for the first cylinder is 300 feet per second, 
the weight of steam per second is 3.15 pounds and thes pecific 
volume at the seventh stage, i.e., the middle of the first barrel, 
is 3.27 cubic feet. The effective area must therefore be 

WV 'l.\^ X S-27 . ^ 

a = 144 -— = 144 - — - — ^ ' =4.94 square mches. 
V 300 

To this must be added a fraction of one-third or one-fourth to 
allow for the thickness of the blades, and the result must be 
divided by sine a in order to find the area of the peripheral 
ring through which the steam will flow. Taking one-fourth 
for the fraction in this case, and 20° for a, we have 

4.94 X 5 o . , 

-^-^-^ ^ = 18.1 square mches. 

0.342 X 4 

It is recommended that the height of the blades shall be 0.03 
of the diameter, which gives for the expression for the peripheral 
ring 

0.03 Tzd"^ = 18. 1. 



.'. d = V 18.1 -^ 0.03 n = 13.85 inches. 

The diameters of the intermediate and low-pressure cylinders 
will be 

d^ = 13.85 X 1.5 = 20.77 in.; d^ = 13.85 X 2^ = 34.62 in. 

The length of blade at the seventh stage will be 

0.03 X 13.85 = 0.415 inch. 



DESIGN FOR A REACTION TURBINE , 525 

and this length will be assigned to all the blades of the first 
barrel. The blades of the second and third barrels will have 
their lengths increased in proportion to the specific volumes at the 
middle of those barrels, as set down in the table. The effect 
of increasing the diameters of the intermediate and low-pres- 
sure cylinders is to increase the steam velocity, and the peripheral 
length of the steam passage, both in proportion to the diameter. 
Consequently the lengths of the blades for these cylinders are 
directly proportional to the proper specific volumes and inversely 
proportional to the squares of the diameters. Thus the length 
of the blades at the forty-second stage, i.e., the middle of the 
fourth barrel is 

0.415 X 9.43 . , 

— ^^-^ ^£^ = 0.532 mch. 

3-27 X 1.5 

The lengths are computed for the other barrels in the same way, 
using 2.5 for the ratio of the low-pressure diameter. 

Since the diameter of the small cylinder is 13.85 inches and 
the speed of the vanes on it is 225 feet per second, the revolutions 
per minute are 

22s X 60 X 12 

Parsons Turbine. — The essential features of the Parsons 
turbine are shown by Fig. 117. Steam is admitted at A and 
passes in succession through the stages on the high-pressure 
cylinder, and thence through the passage at E to the stages of 
the intermediate cylinder; after passing through the intermediate 
stages it passes through G to the low-pressure stages and finally 
by B to the condenser. 

The axial thrust is counterbalanced by the dummy cylinders, 
C, C, C, the first receiving steam from the supply directly, the 
second from the passage between the high and intermediate 
cylinders through the pipe F, and the third through the pipe near 
G from the passage between the intermediate and low-pressure 
cylinders. Leakage past the dummy cylinders is checked by laby- 
rinth packing, which is variously arranged to give a succession 



S26 



STEAM-TURBINES 




Fig. 117. 



of spaces through which the steam must pass with narrow pass- 
.ages, which throttle the steam as it passes from chamber to 
chamber. One method is to let narrow strips of brass into 
the surface of the cylinder and into the surface of the case; 
these strips are adjusted to leave a very small axial clearance, 
so that the steam is strongly throttled as it passes through. It 
is reported that the labyrinth clearance is entirely successful in 
reducing the leakage past the dummy cylinder to a small amount. 
It is pointed out by Mr. Jude that the most effective throttling 
is at the last section of the labyrinth, and that the other sections 
are comparatively inefficient. This feature will be evident if an 
attempt is made to calculate the loss by continual application of 
Rankine's equations, page 432. Of course such a method can be 
but crude, and yet its indications should be of value for estimating 
leakage which should be small. 

When applied to marine propulsion the dummy pistons are 
omitted and the axial thrust is usefully applied to the propeller- 
shaft. Since an absolute balance cannot be obtained, a thrust- 
bearing is provided but it may have small bearing area and will 
have but little friction. Stationary turbines also have a bearing 
for residual unbalanced thrust. 

Test on a Parsons Turbine. — A test on a Westinghouse- 



TEST ON A PARSONS TURBINE 



527 



Parsons turbine in Savannah was made under the direction of 
Mr. B. R. T. Collins and reported by Messrs. H. O. C. Isenberg 
and J. Lage,* which is interesting because the steam consumption 
of the auxiliary machines was determined separately. The 
data and results of tests on the turbine are given in the following 
table. 

The tests made at full load with varying degrees of vacuum 
show clearly the advantage obtained in this machine from a 
good vacuum, which amounted to a saving of 



289 — 279 _ 
289 



0-035- 



TESTS ON WESTINGHOUSE-PARSONS TURBINE. 
Collins, Isenberg and Lage. 



Duration minutes 

Steam pressures, gauge . 

Vacuum inches 

Revolutions per minute . . 

Load kilowatts 

Steam consumption, pounds 

per kilowatt-hour .... 

per electric h.p. per hour . 
Heat consumption b.t.u. 

per kilowatt-minute 

per horse-power per minute 



i load. 


J load. 


Full load. 


ij load. 


60 


60 


60 


60 


60 


45 


131 
28.1 
3616 
260 


129 
28.1 
3601 

379 


128 

25-7 
3602 

493 


127 
26.7 
3612 
501 


128 
28.0 
3562 
499 


127 
26.7 
3540 
629 


243 
18. 1 


21.2 
15-8 


20.7 
15,6 


19.8 
14.8 


19.7 
14.7 


19.8 
14.7 


462 
345 


403 
301 


494 
289 


375 
284 


374 
279 


373 
278 



li load. 



45 
125 
26.6 

3537 
733 

20. 2 
15-1 



381 
283 



A great importance is attributed by turbine builders to obtaining 
a low vacuum, in many cases special air-pumps and other devices 
being used for that purpose. Unless discretion is shown both 
in the design and operation of this auxiliary machinery, its size 
and steam consumption is likely to be excessive, and what appears 
to be gained from the vacuum may be entirely illusory. 



* Thesis, M.I.T. 1906. 



528 STEAM-TURBINES 

The steam consumption in pounds per hour for the several 
auxiliary machines was as follows: 

Centrifugal pump for circulating water .... 88i 

Dry vacuum pump 212 

Hot-well pump 42.8 

II35-8 

This total was equivalent to 0.115 of the steam consumption 
of the turbine at full load and with 28 inches vacuum. Some 
tests of turbine installations show twice or three times this 
proportion. 



INDEX. 



PAGE 

Absolute temperature 56 

Absorption refrigerating apparatus 411 

Adiabatic for gases 63 

for liquid and vapor 100 

lines 17 

Adiabatics, spacing of 31 

After burning 319 

Air-compressor, calculation ... 377 

compound 366 

cooling during compression . . 360 

effect of clearance 363 

efficiency 370 

friction 369 

fluid piston 359 

moisture in cylinder 361 

power expended 362 

three-stage 368 

Air, flow of 429 

friction in pipes 380 

pump 374,375 

thermometer 368 

Alternative method 49 

Ammonia 123 

Automatic and throttle engines . 276 

Bell-Coleman refrigerating ma- 
chine 413 

Binary engines 180, 280 

Blast-furnace gas-engine .... 335 

Boyle's law 54 

British thermal unit 5 

Buchner 437 

Calorimeter 191 

separating 194 

Thomas 195 

throttling 161 

Calorie 5 

Callendar and Nicolson .... 231 



PAGE 

Carnot's engine 22 

function 28 

principle 26 

Characteristic ec] nation 2 

for gases 55 

for superheated vapors .... no 

Chestnut Hill, engine test .... 239 

Compound air-compressor . . . 366 

air-engine 384 

Compound-engines 156 

cross-compound 169 

direct-expansion 163 

indicator diagrams 162 

low-pressure cut-off 161 

ratio of cylinders 162 

total expansions r6o 

with receiver 159 

without receiver . .' 158 

Compressed-air 358 

calculation 377 

compound compressor .... 366 

effect of clearance 363 

friction, etc 369 

hydraulic compressor .... 372 

interchange of heat 365 

storage of power 392 

temperature after compression . 364 

transmission of power .... 391 

Compressed-air engine 384 

calculation 388 

compound 388 

consumption 385 

final temperature 385 

interchange of heat 386 

moisture in cylinder 3O1 

volume of cylinder 386 

Condensers 149 

cooling surface 151 

ejector 471 

529 



530 



INDEX 



PAGE 

Carburetors 334 

Creusot, tests on engine .... 248 

Critical temperature 71 

Cut-off and expansion 273 

Cycle, closed 25 

non-reversible 40 

reversible 24 

Delafond 248 

Oenton 4i9.»20 

Density at high-pressure .... 71 

Dry ness-f actor 86 

Designing steam-engines . . 152, 179 

Diesel motor 341 

economy 355 

Differential coefl&cient dpfdt . . 79 

Dixwell's tests 270 

Dynamometers 186 

Economy, methods of improving. 245 

compounding 257 

expansion 256 

increase of size 255 

intermediate reheaters .... 268 

of steam-engines 237 

raising pressure 247 

steam-jackets 261, 266 

superheating 270 

variation of load 274 

Effectof raising steam-pressure, 148, 247 

Efficiency 25 

mechanical 287 

of reversible engines ^^ 

of steam-engine 130, 144 

P^fficiency, maximum 39 

of superheated steam .... 115 

Ejector 470 

condenser 471 

P^ngine, Carnot's 22 

compressed-air 384 

friction of 285 

hot-air 298 

internal combustion 298 

«il 335 

reversible 24 

P^ntropy 000 



VAGB 

Entropy — Continued. 

due to vaporization 99 

expression for 35 

of a liquid 97 

of a liquid and vapor .... 99 

of gases 67 

scale of 31 

Exponential equation 66 

First and second laws combined 49 

First law of thermodynamics 13 

application of 45 

application of vapors 88 

Flow in tubes and nozzles . . . 434 

Buchner's experiments .... 437 

design of a nozzle 444 

experiments 436 

friction head 435 

Kneass' experiments 440 

Kuhhardt's experiments . . . 443 

Lewicki's experiments .... 442 

Rateau's experiments .... 440 

Rosenhain's experiments . . ' 441 

Stodola's experiments .... 441 

Flow of air, Fliegner's equations . 429 

in pipes 380 

maximum velocity 430 

through porous plug 69 

P'low of fluids 423 

of gases 426 

of incompressible fluids . . . 425 

of saturated vapor 430 

of superheated steam .... 433 

French and English units .... 56 

Friction of engines 285 

distribution 295 

initial and load 287 

Gas-engine 304 

after burning 319 

blast-furnace gas 333 

economy and efficiency . . 320, 348 

ignition 329 

starting devices 329 

temperature after explosion . . 318 

valve-gear 324 

water jackets 320 



INDEX 



531 



I'AGi; 

Gas-engines — Continued. 

with compression in cylinder . 308 

with separate compression . . 305 

(ias-engines four-cycle 337 

two-cycle 338 

Cjases 54 

adiabatic equations 64 

characteristic equation .... 55 

characteristics for gas-engines . 314 

entropy 67 

general equations 61 

intrinsic energ)' 66 

isoenergic equation 63 

isothermal equation 61 

special method 60 

specific heats 59 

specific volumes 57 

Gasoline engine 334 

Gas-producers 331^352 

Gauges 186 

Gay-Lussac's law 54 

( xraphical representation of change 

of energy 20 

of characteristic equation ... 4 

of efficiency 33 

(irashoff's formula 432 

Hall's investigations 230 

Hallauer's tests 219 

Heat of the liquid 82 

Heat of vaporization 85 

Him engine, tests on 220 

Hirn's analysis 205 

Hot-air engines 298 

Ignition 329 

Indicators 187 

Influence of cylinder walls ... 199 

Callendar and Nicolson ... 231 

Hall 230 

Hirn's analysis 205 

representation 202 

Injector 447 

combining-tube 458 

delivery-tube 459 

double 461 



PAGU 

Injector — Continued. 

efliciency of 459 

exhaust steam 467 

Korting 462 

lifting 460 

restarting 464 

self-adjusting 462 

Seller's 460 

steam-nozzle 458 

theory 448 

velocity in delivery tube ... 455 

velocity of steam -jet 452 

velocity of water 454 

Internal combustion engines . . 298 

Internal latent heat 87 

Intrinsic energy 14 

of gases 66 

of vapors 95 

Isoenergic or isodynamic line . . 17 

for gases 63 

Isothermal lines 16 

for gases 61 

for vapors 94 

Josse, tests on binary engine . . 282 

Joule and Kelvin's experiments . 69 

Kelvin's graphical method ... 29 

Kerosene-oil engine 335 

Kilogram 56 

Kneass 440-452 

Knoblauch no 

Kuhhardt 443 

Latent heat of expansion ... 6 
Laws of thermodynamics . . . 13, 22 

application to gases 59 

application to vapors 88 

Lewicki . . '. 442 

Lines, adiabatic 17 

isoenergic 17 

isothermal 16 

of equal pressure 16 

of equal volume 16 

Meyer 350 

Mass. Inst. Technology, engine 

tests 262 



532 



INDEX 



PAGE 

Mechanical efficiency 286 

Mechanical equivalent of heat . . 8t 

Meter ..." 56 

Non-reversible cycles 40 

Oil-engine economy 355 

Oil-engines 335 

Porous plug, flow through ... 69 

Pressure of saturated steam ... 77 

of vapors 77 

specific 2 

Quality 86 

Rankine's equations for flow of 

steam 432 

cycle 134 

Rateau 440 

Ratio of cylinders, compound en- 
gines 162 

Refrigerating machines 396 

absorption 411 

air 396 

calculations for 403, 408 

compression 405 

fluids, for 409 

proportions 398, 406 

tests 412, 413, 417 

vacuum 398 

Regnault's equations for steam . 77 

Relations of thermal capacities . 12 

of adiabatics and isothermal lines 18 

Reversible cycle 24 

engine 24 

Rontgen's experiments 72 

Rosenhain 441 

Rowland 81 

Saturated vapors 76 

adiabatic equations 100 

entropy 97> 99 

flow of 430 

general equation 87 

intrinsic energy 95 

isoenergic equation 95 

isothermal equation 94 



pac;e 

Saturated vapors — Continued. 

pressure of 77 

specific heats 93 

specific volumes 91 

Saturated vapors, special method . 90 
Schroter's tests of refrigerating 

machines 412, 417 

tests of steam-engines .... 273 
Seaton's multipliers for steam- 
engine design 179 

Second law of thermodynamics 22, 27 

application of 47 

application to vapors 89 

Specific-heat 6, 58 

of gases 58 

of liquids 83 

of superheated steam .... 93 

of water 80 

Specific -heats, ratio of 59 

Specific -pressure 56 

Specific-volume 3 

of gases 57 

of liquids 85 

of vapors 91 

Starting devices 325 

Steam-engine 128 

actual 142 

Carnot's cycle 128 

compound 156 

designing 152, 179 

economy 245 

efficiency 130 

Hirn's analysis 205 

indicators 187 

influence of the cylinder walls . 190 

leakage of valves 234 

variation of load 274 

Seaton's multipliers 179 

triple-expansion 172 

with non-conducting cylinder . 134 

Steam turbines 47^ 

compound 4^6 

compounding velocity .... 487 

" pressure .... 493 

" pressure and velocity 506 



INDEX 



533 



PAGE 

Steani turbines — Continued. 

Curtis 513 

effect of friction .... 481, 491 

impulse , . 473 

" general care .... 477 

friction of rotating disks . . 504 

lead 502 

leakage and radiation .... 501 

noaxial thrust 480 

Rateau 503 

reaction 476, 515, 520 

Stirling's hot-air engine .... 299 

Stodola 441 

Sulphur dioxide 117 

Superheated vapors no 

characteristic equation .... 121 

entropy 115 

specific-heat 112 

total heat 114 

Temperature 3 

absolute scale 29 

standard 5, 81 

Temperature-entropy diagram 

35, 104, 131, 137 
table 106, 139 



PAGE 

Testing steam-engines 183 

Tests of steam-engines 237 

examples of economy .... 238 

marine engines 241, 242 

simple engines 250 

steam-pumps 244 

superheated steam .... 270, 273 

Thermal capacities 1,7 

of gases 61 

relations of 9 

Thermal lines 16 

and their projections .... 19 

Thermal unit 5 

Thomas 112 

Thurston 294 

Total heat of steam 84 

of superheated steam .... 114 

of vapors . 85 

Triple-expansion engines .... 172 

Tumlirz in 

Value of i? 57 

Waste-heat engine 357 

Weirs 191 

Zeuner's equations . 51 



OCT 1^'inn7 



